{"id":24450,"date":"2023-05-12T12:25:31","date_gmt":"2023-05-12T06:55:31","guid":{"rendered":"https:\/\/apboardsolutions.in\/?p=24450"},"modified":"2023-05-12T17:21:34","modified_gmt":"2023-05-12T11:51:34","slug":"ap-board-5th-class-maths-solutions-5th-lesson","status":"publish","type":"post","link":"https:\/\/apboardsolutions.in\/ap-board-5th-class-maths-solutions-5th-lesson\/","title":{"rendered":"AP Board 5th Class Maths Solutions 5th Lesson Multiples and Factors"},"content":{"rendered":"

Andhra Pradesh AP Board 5th Class Maths Solutions<\/a> 5th Lesson Multiples and Factors World Textbook Exercise Questions and Answers.<\/p>\n

AP State Syllabus 5th Class Maths Solutions Chapter 5 Multiples and Factors<\/h2>\n

Question 1.
\nObserve which numbers are not divisible?<\/p>\n

\"AP<\/p>\n

Answer: Which of the above numbers are exactly divisible by 2?
\nAnswer:
\n2410, 1282, 3784, 6728, 5466<\/p>\n

b. Observe the units place of the numbers which are divisible by 2.
\nAnswer:
\n0, 2, 4, 6, 8.<\/p>\n

c. Are all these numbers even numbers ? Yes \/ no. (Yes)
\nAnswer:
\nSo a number is divisible by 2, if the digit at its one place is either 0\/2\/4\/6\/8.<\/p>\n

\"AP<\/p>\n

Do these: (TextBook Page No.62)<\/span><\/p>\n

Question 1.
\nCircle the following numbers which are divisible by 2.<\/p>\n

\"AP<\/p>\n

Answer:<\/p>\n

\"AP<\/p>\n

Question 2.
\nWrite any 5, four-digit numbers which arc divisible by 2 ?
\nAnswer:
\n25680, 45,622, 78,964, 87,766 and 97.678<\/p>\n

Exercise 1:<\/span><\/p>\n

Question 1.
\nFind the numbers which are divisible by 2. Write the reason for the numbers which are not divisible?
\na) 3458
\nb)56745
\nc) 3850
\nd) 6736
\ne) 6733
\nf) 3394
\nAnswer:
\n3458, 3850, 6736 and 3394 are divisible by 2. Remaining numbers are not divisible.
\nReason : The digits of the numbers of ones places is 3 and 5.<\/p>\n

\"AP<\/p>\n

Question 2.
\nFind the numbers which are divisible by 5 and 19. Write the reason for the numbers which are not divisible ?
\na) 3568
\nb) 3540
\nc) 6585
\nd) 7550
\ne) 4235
\nf) 7200
\ng) 7865
\nh) 5880
\ni) 4440
\nj) 8198
\nk) 8645
\nAnswer:
\nb, d, f, h, j are divisible by both 5 and 10. Remaining numbers are not divisible by 5 and 10.
\nReason : The numbers which have n’t zero at their ones place.<\/p>\n

Question 3.
\nThe numbers below are divisible by 5. Fill in the blanks with suitable digit.
\na) 786_
\nAnswer:
\n786_ (0\/5)<\/p>\n

b)560_
\nAnswer:
\n560_(0\/5)<\/p>\n

c)785_
\nAnswer:
\n785_(0\/5)<\/p>\n

d) 555_
\nAnswer:
\n555_ (0\/5)<\/p>\n

e) 586_
\nAnswer:
\n586(0\/5)<\/p>\n

f) 786_
\nAnswer:
\n786_(0\/5)<\/p>\n

g) 584_
\nAnswer:
\n584_(0\/5)<\/p>\n

h) 100_
\nAnswer:
\n100_(0\/5)<\/p>\n

Question 4.
\nWrite any 5 numbers which are exactly divisible by 2 and 5.
\nAnswer:
\n2540, 62570, 250, 367280 and 764520.<\/p>\n

Question 5.
\nWrite any 5 numbers which are exactly divisible by 2,5 and 10 ?
\nAnswer:
\n86540, 79980, 89960, 45570 and 76540.<\/p>\n

\"AP<\/p>\n

Do these: (TextBook Page No.65)<\/span><\/p>\n

Question 1.
\nCircle the number which is exactly divisible by 3 and 9 and write correct reason.<\/p>\n

\"AP<\/p>\n

Answer:<\/p>\n

\"AP<\/p>\n

Reason : If the digital root of the given number is 9, then the number is exactly divisible by 3 and 9.<\/p>\n

Question 2.
\nWrite any 5 numbers which are exactly divisible by 3 and 9?
\nAnswer:
\n1350, 1476, 0342, 1539 and 1629.<\/p>\n

Do these: (TextBook Page No.66)<\/span><\/p>\n

Question 1.
\nCircle the numbers which are divisible by 4. Give the reason, if is not divisible by 4.<\/p>\n

\"AP<\/p>\n

Answer:<\/p>\n

\"AP<\/p>\n

a, b, d, f and g are divisible by 4. Remaining numbers last two digits is not divisible by 4. So they are not divisible by 4.<\/p>\n

Question 2.
\nWrite the missing number in the blank to make the number exactly divisible by 4.
\na) 323_
\nAnswer:
\n323_ (2 \/ 6)<\/p>\n

b) 304_
\nAnswer:
\n304_ (0)<\/p>\n

c) 58_6
\nAnswer:
\n58_ 6 (1\/3)<\/p>\n

d) 53_ _
\nAnswer:
\n53_ _ (04 \/ 0812 \/ 16 \/ 20 \/ 24 \/ 28 \/ 36\/ 40)<\/p>\n

e) 65_ _
\nAnswer:
\n65_ _
\n(04 \/ 08 \/ 12 \/ 16 \/ 20 \/ 24 \/ 28\/ 36 \/ 40).<\/p>\n

\"AP<\/p>\n

Do these (Textbook Page No. 67)<\/span><\/p>\n

Question 1.
\nCheck whether the following numbers are divisible by 6 or not.
\n1) 210
\n2) 162
\n3) 625
\n4) 120
\n5) 156
\nAnswer:
\n210, 162, 120 and 156 are divisible by \u20196\u2019.<\/p>\n

Question 2.
\nChange the digits of the following numbers to make them divisible by 6.
\n1) 543
\n2) 231
\n3) 5463
\n4) 1002
\n5) 4815
\nAnswer:<\/p>\n

\"AP<\/p>\n

Do these: (TextBook Page No.68)<\/span><\/p>\n

Question 1.
\nFind the following numbers which are divisible by 8.
\na) 2456
\nb) 3971
\nc) 824
\nd) 923
\ne) 2780
\nf) 93624
\ng) 76104
\nAnswer:
\na) In 2456, 456 is divisible by 8. So, 2456 is divisible by 8.
\nb) In 3971, 971 is not divisible by 8. So, 3971 is not divisible by 8.
\nc) 824 is divisible by 8.
\nd) 923 is not divisible by 8.
\ne) In 2780, 780 is not divisible by 8. So, 2780 is not divisible by 8.
\nf) In 93624, 624 is divisible by 8. So, 93624 is divisible by 8.
\ng) In 76104, 104 is divisible by 8. So, 76104 is divisible by 8.<\/p>\n

\"AP<\/p>\n

Exercise 2:<\/span><\/p>\n

Question 1.
\nCircle the following numbers which are divisible by 2 (by using divisibility rule).
\n3624<\/span> 3549<\/span> 7864<\/span> 8420<\/span> 8500<\/span> 8646<\/span> 5007<\/span> 7788<\/span>
\nAnswer:<\/p>\n

\"AP<\/p>\n

Question 2.
\nFind out which of the following numbers are divisible by 6.
\n1276 43218 71218 71826 4734 3743
\nAnswer:
\n(i) Given number = 1276
\nOnes place is 6 that is even.
\n1276 is divisible by 2.
\nDigital root of 1276 is 1 + 2 + 7 + 6 = 16
\n16 is not divisible by 3.
\nSo, 1276 is not divisible by 6.<\/p>\n

(ii) Given number = 43218
\nOnes place is 8 that is even.
\n43218 is divisible by 2.
\nDigital root of 43218 is 4 + 3 + 2 + 1 + 8 = 18
\n18 is divisible by 3.
\nSo, 43218 is divisible by ‘6’.<\/p>\n

(iii) Given number = 71218
\nOnes place is 8 that is even.
\n71218 is divisible by ‘2’
\nDigital root of 71218 is
\n7 + 1 + 2 + 1 + 8 = 19
\n19 is not divisible by ‘3’
\nSo, 71218 is divisible by ‘6’.<\/p>\n

(iv) Given number = 71826
\nOnes place is ‘6’ that is even.
\n71826 is divisible by ‘2’
\nDigital root of 71826 is 7 + 1 + 8 + 2 + 6 = 24
\n24 is divisible by ‘3’
\nSo, 71826 is divisible by’6′.<\/p>\n

(v) Given number = 4734
\nOnes place is ‘4’ that is even.
\n4734 is divisible by ‘2’
\nDigital root of 4734 is 4 + 7 + 3 + 4 = 18
\n18 is divisible by’3′
\nSo, 4734 is divisible by ‘6’.<\/p>\n

(vi) Given number = 3743
\nOnes place is ‘3’ that is odd.
\n3743 is not divisible by ‘2’
\nSo, 3743 is not divisible by ‘6’.<\/p>\n

\"AP<\/p>\n

Question 3.
\nThe number 50 \"AP 9 is exactly divisible by 9. Fill the \"AP with the correct number.
\nAnswer:
\nGiven number 50 \"AP 19 is exactly divisible by 9.
\nSo, digital root is 5 + 0 + ? + 1 + 9 = 15 + ?
\n= 15 + 3 = 18 = 1 + 8 = 9
\n\u2234 9 is divisible by ‘9’.<\/p>\n

Question 4.
\nThe number 4 \"AP 468 is exactly divisible by 6. Fill the \"AP with the correct number.
\nAnswer:
\nGiven number 4 \"AP 468 is exactly divisible by 6. So, digital roots is 4 + \"AP + 4 + 6 + 8 = 22 + 2 = 24
\n24 is divisible by 3.
\nSo, 4 2 468 is divisible by 6.<\/p>\n

Question 5.
\nFill the blanks with suitable digits. So that it can be divisible by 2 and 10.
\n678_ 588_ 388_ 222_
\n364_ 786_ 666_ 788_
\nAnswer:
\nGiven numbers are divisible by ’10’ they have ‘0’ in its units place and that number also divisible by ‘2’.
\n6780<\/span> 5880<\/span> 3880<\/span> 2220<\/span>
\n3640<\/span> 7860<\/span> 6660<\/span> 7880<\/span><\/p>\n

Question 6.
\nFind the numbers which are divisible by 4 and 8.
\n2104 726352 1800 32256 52248 25608
\nAnswer:
\nObserve the last two digits of the given numbers 2104, 726352, 1800, 32256, 52248 and 25608.
\nThere are 04, 52, 00, 56, 48 and 08 at the end of the numbers.
\nHence all these numbers are multiples of 4.
\nSo, 2104<\/span>, 726352<\/span>, 1800<\/span>, 32256<\/span>, 52248<\/span> and 25608<\/span> are divisible by 4.<\/p>\n

Divisible by 8 :
\ni) Given number 2104
\nLast three digits of given 104 is divisible by 8.
\nSo, 2104 is divisible by 8.<\/p>\n

ii) Given number 726352
\nLast three digits of given 352 is di-visible by 8.
\nSo, 726352 is divisible by 8.<\/p>\n

iii) Given number 1800
\nLast three digits of given 800 is divisible by 8.
\nSo, 1800 is divisible by 8.<\/p>\n

iv) Given number 32256
\nLast three digits of given 256 is divisible by 8.
\nSo, 32256 is divisible by 8.<\/p>\n

v) Given number 52248
\nLast three digits of given 248 is divisible by 8.
\nSo, 52248 is divisible by 8.<\/p>\n

\"AP<\/p>\n

Question 7.
\nTry whether the numbers are divisible by 2, 3, 4, 5, 6, 8, 9 and 10.
\na) 333
\nb) 128
\nc) 225
\nd) 7535
\ne) 8289
\nf) 99483
\ng) 67704
\nh) 67713
\ni) 9410
\nj) 67722
\nk) 20704
\nl) 35932
\nm) 85446
\nn) 90990
\no) 18540
\nAnswer:
\na) Given number is 333
\nDigital root of 333 is 3 + 3 + 3 = 9
\nHence it is multiple of 3 and 9.
\nSo, 333 is divisible by 3 and 9.<\/p>\n

b) Given number is 128.
\nOnes place is 8 that is even.
\n128 is divisible by 2.
\nLast two digits of the given number is 28 is multiple of 4.
\nSo, 128 is divisible by 4.
\n128 \u00f7 8 = 16.
\nSo, 128 is divisible by 8
\nHence 128 is divisible by 2, 4 and 8.<\/p>\n

c) Given number is 225
\nOnes place is ‘5’, so it is divisible by 5.<\/p>\n

d) Given number is 7535
\nOnes place is 5, so, it is divisible by 5.<\/p>\n

\"AP<\/p>\n

e) Given number is 8289.
\nDigital root of 8289 is 8 + 2 + 8 + 9 = 27 = 2 + 7 = 9
\n9 is multiple of 3 and 9.
\nSo, 8289 is divisible by 3 and 9.<\/p>\n

f) Given number is 99483.
\nDigital root of 99483 is 9 + 9 + 4 + 8 + 3 = 33 = 3 + 3 = 6
\n6 is multiple of 3, so, 99483 is divisible by 3.<\/p>\n

g) Given number is 67704
\nOnes place is 4 that is even.
\n67704 is divisible by 2.
\nDigital root of 67704 is 6 + 7 + 7 + 0 + 4 = 24 = 2 + 4 = 6.
\n6 is multiple of 3, so, 67704 is divisible by 3.
\nThe number is divisible by 2 and 3, so, 67704 is divisible by 6.
\nLast two digits of the number is 04 is divisible by 4. So, 67704 is divisible by 4.
\nLast three digits of the number is 704 is divisible by 8.
\nSo, 67704 is divisible by 8.
\n\u2234 67704 is divisible 2, 3,4, 6 and 8.<\/p>\n

h) Given number is 67713
\nDigital root of 67713 is 6 + 7 + 7 + 1 + 3 = 24 = 2 + 4 = 6
\n6 is multiple of 3.
\nSo, 67713 is divisible of 3.<\/p>\n

i) Given number is 9410
\nLast digit of given number is ‘0’ that is even.
\nSo, 9410 is divisible by 2, 5 and 10.<\/p>\n

j) Given number is 67722
\nOnes place is 2 that is even.
\n67722 is divisible by 2.
\nDigital root of 67722 is 6 + 7 + 7 + 2 + 2 = 24 = 2 + 4 = 6
\n‘6’ is divisible by 3.
\nSo, 67722 is divisible by 6.<\/p>\n

k) Given number is 20704.
\nOnes place is 4 that is even.
\n20704 is divisible by 2.
\nLast two digits of the number is 04 is divisible by 4.
\nSo, 20704 is divisible by 4.
\nLast three digits of the number is 704 is divisible by 8. So, 20704 is divisible by 8.
\n\u2234 20704 is divisible 2, 4 and 8<\/p>\n

l) Given number is 35932
\nOnes place is 2 that is even.
\n35932 is divisible by 2.
\nLast two digits of the number is 32
\n32 is multiple of 4.
\nSo, 35932 is divisible by 4.
\n\u2234 35932 is divisible 2 and 4<\/p>\n

m) Given number is 85446
\nOnes place is 6 that is even.
\n85446 is divisible by 2.
\nDigital root of 85446 is 8 + 5 + 4 + 4 + 6 = 27 = 2 + 7 = 9
\n\u2234 ‘9’ is multiple of 3 and 9.
\nSo, 85446 is divisible by 3 and 9.
\n\u2234 85446 is divisible by 2,3 and 9.<\/p>\n

n) Given number is 90990
\nLast digit is ‘0’.
\nSo, it is divisible by 2,5 and 10.<\/p>\n

o) Given number is 18540 Last digit is ‘0’.
\nSo it is divisible by 2, 5 and 10.<\/p>\n

\"AP<\/p>\n

Question 8.
\nFind the missing digit that would make each number divisible by the given number.
\na) 395 _ by 10
\nAnswer:
\n395 0<\/span><\/p>\n

b)24305 _ by 9
\nAnswer:
\n24305 4<\/span><\/p>\n

c) 69839 _ by 3 and 9
\nAnswer:
\n698391<\/span><\/p>\n

d) 271 _ 8 by 6
\nAnswer:
\n2710<\/span> 8<\/p>\n

e) 20710 _
\nAnswer:
\n20710_<\/p>\n

f) 5027 _ 5 by 3 and 5
\nAnswer:
\n50273<\/span> 5<\/p>\n

g) 145 _ 2 by 8
\nAnswer:
\n1451<\/span>2<\/p>\n

h) 92048 _ by 2
\nAnswer:
\n92048 _ (0\/2\/4\/6\/8)<\/p>\n

i) 23405 _ by 5
\nAnswer:
\n(0\/5)<\/p>\n

Answer: For eiven ‘e’ problem divisible by is not given. So, the problem is not solved.<\/p>\n

\"AP<\/p>\n

Question 9.
\nFind the smallest number that is to be added to 289279, so that it can be divisible by 8.
\nAnswer:
\nGiven number is 289279.
\nLast three digits of given number is 279.
\n279 is not divisible by 8, but 280 is divisible by 8.
\n289279 is added by 1 it is divisible by 8.<\/p>\n

Do these: (TextBook Page No. 69 & 70)<\/span><\/p>\n

Question 1.
\nWrite first ten multiples of the following.
\na) 3 b) 5 c) 8 d) 9 e) 10
\nAnswer:
\na) Ten multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
\nb) Ten multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
\nc) Ten multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80
\nd) Ten multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90
\ne) Ten multiples of 10 = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100<\/p>\n

Question 2.
\nFind out the multiples of 2, 3, 5 from 1 to 20. Write separately.
\nAnswer:
\nFirst 1 to 20 multiples of 2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
\nFirst 1 to 20 multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
\nFirst 1 to 20 multiples of 5 = 5, 10, 15,20<\/p>\n

Question 3.
\nWrite down the first 10 multiples of 7.
\nAnswer:
\nFirst 10 multiples of 7 is = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70.<\/p>\n

Question 4.
\nFind out the multiples of 7, 8, 10 from the following numbers and write separately.
\n20, 14, 45, 24, 32, 35, 90, 8, 7, 10, 441, 385
\nAnswer:
\nMultiples of 7 from given = 7, 14, 35, 385, 441
\nMultiples of 8 from given = 8, 24, 32
\nMultiples of 10 from given = 10, 20, 90<\/p>\n

Question 5.
\nFind out the numbers which are not the multiples of 3.<\/p>\n

\"AP<\/p>\n

Answer:
\n8 26 32 28 88 48<\/p>\n

Question 6.
\nWrite the odd multiples of 9 less than hundred.
\nAnswer:
\n9, 27, 45, 63, 81, 99.<\/p>\n

\"AP<\/p>\n

Do these: (TextBook Page No.71)<\/span><\/p>\n

Question 1.
\nWrite first 10 multiples of the following numbers and list the com-mon multiples.
\na) 2 and 4
\nb) 4 and 12
\nc) 6 and 8
\nd) 5 and 10
\nAnswer:
\na) Multiples of 2 : 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.
\nMultiples of 4 : 4, 8, 12, 16, 20, 24, 28, 32, 36, 40
\nCommon multiples of 2 and 4 : 4, 8, 12, 16, 20<\/p>\n

b) Multiples of 4 : 4, 8, 12, 16, 20, 24, 28, 32, 36, 40
\nMultiples of 12 : 12, 24, 36, 48, 60, 72, 84, 96, 108, 120
\nCommon multiples of 4 and 12 : 12, 24, 36<\/p>\n

c) Multiples of 6 : 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
\nMultiples of 8 : 8, 16, 24, 32, 40, 48, 56, 64, 72, 80
\nCommon multiples of 6 and 8 : 24, 48<\/p>\n

d) Multiples of 5 : 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
\nMultiples of 10 : 10, 20, 30, 40, 50, 60, 70, 80, 90, 100
\nCommon multiples of 5 and 10 : 10, 20, 30, 40, 50.<\/p>\n

\"AP<\/p>\n

Do this: (TextBook Page No. 72)<\/span><\/p>\n

Find the LCM for the following sets of numbers.
\nAnswer:
\nMultiples of 12 : 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, …………..
\nMultiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, …………
\nCommon multiples of 12 and 15 = 60, 120
\nLeast common multiple of 12 and 15 = 60.<\/p>\n

2) Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144, 160
\nMultiples of 20 : 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, ………..
\nCommon multiples of 16 and 20 = 80, 160.
\nLeast common multiple of 16 and 20 = 80<\/p>\n

3) Multiples of 8:
\n8, 16, 24, 32, 40, 48, 56, 64, 72, 80, ……….., 120, ………..
\nMultiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, …………
\nMultiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, …………
\nLeast common multiple of 16 and 20 = 80
\nCommon multiples of 8, 12 and 20 = 120
\nLeast common multiple of 8, 12 and 20 = 120<\/p>\n

4) Multiples of 15 : 15, 30, 45, 60, 75, 90, 105, 120, 135, 150 ……….
\nMultiples of 20 : 20, 40, 60, 80, 100, 120, 140, 160, 180, 200
\nCommon multiples of 15 and 20 = 60, 120
\nLeast common multiple of 15 and 20 = 60<\/p>\n

5) Multiples of 6 : 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, …………
\nMultiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, ………..
\nMultiples of 12 : 12, 24, 36, 48, 60, 72, 84, 96, 108, 120
\nCommon multiples of 6, 9 and 12 = 36
\nLeast common multiple of 6, 9 and 12 = 36.<\/p>\n

\"AP<\/p>\n

Try this: (TextBook Page No. 72)<\/span><\/p>\n

Find the LCM for the following pairs of numbers. What do you ob-serve.
\n1) 15, 30
\n2) 4, 16
\n3) 5, 15
\n4) 6, 18
\nAnswer:
\n1) Multiples of 15 : 15, 30, 45.60. 75.90, 105, 120, 135,150
\nMultiples of 30 : 30,60, 90. 120, 150, 180, 210, 240, 270, 300, …………
\nCommon multiples of 15 and 30
\n30, 60, 90, 120, 150, ……………..
\nLeast common multiples of 15 and 30 = 30<\/p>\n

2) Multiples of 4 :
\n4, 8, 12, 16, 20, 24, 28, 32, 36, 40, …………
\nMultiples of 16 : 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, …………..
\nCommon multiples of 4 and 16 = 16, 32, 48 …………
\nLCM of 4 and 16 = 16<\/p>\n

3) Multiples of 5 : 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, …………..
\nMultiples of 15 : 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, ………….
\nCommon multiples of 5 and 15 = 15, 30, 45, 60
\nLCM of 5 and 15 = 15<\/p>\n

4) Multiples of 6 :
\n6, 12, 18,24, 30, 36,42,48, 54, 60, ……………
\nMultiples of 18 :
\n18, 36, 54, 72,90, 108, 126, 144, 162, 180, ……….
\nCommon multiples of 6 and 18 = 18, 36, 54
\nLCM of 6 and 18 = 18
\nObservation :
\nIn a given pair of numbers, if one of them is multiple of other number than the biggest number is LCM of the number.<\/p>\n

\"AP<\/p>\n

Do these: (TextBook Page No.75)<\/span><\/p>\n

Question 1.
\nFind all the factors of the following numbers.
\na) 21
\nb) 38
\nc) 72
\nd) 96
\nAnswer:
\na) 21 = 1 \u00d7 21 = 3 \u00d7 7 = 7 \u00d7 3 = 21 \u00d7 1
\nThus, all the factors of 21 are : 1, 3, 7 and 21.<\/p>\n

b) 38 = 1 \u00d7 38
\n= 2 \u00d7 19
\nThus, all the factors of 38 are : 1, 2, 19 and 38.<\/p>\n

c) 72 = 1 \u00d7 72
\n= 2 \u00d7 36
\n= 3 \u00d7 24
\n= 4 \u00d7 18
\n= 6 \u00d7 12
\n= 8 \u00d7 9
\nThus, all the factors of 72 are : 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.<\/p>\n

d) 96 = 1 \u00d7 96
\n= 2 \u00d7 48
\n= 3 \u00d7 32
\n= 4 \u00d7 24
\n= 6 \u00d7 16
\n= 8 \u00d7 12
\nThus, all the factors of 96 are : 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48 and 96.<\/p>\n

\"AP<\/p>\n

Question 2.
\nFind out whether the first number is a factor of the second number.
\na) 14; 322
\nb) 26; 832
\nc) 35; 425
\nd) 56; 3500
\ne) 8; 48
\nf) 14; 37
\ng) 15; 75
\nh) 12; 72
\nAnswer:
\na) Yes, 14 is a factor of 322.
\nb) Yes, 26 is a factor of 832.
\nc) No, 35 is not a factor of 425.
\nd) No, 56 is not a factor of 3500.
\ne) Yes, 8 is a factor of 48.
\n0 No, 14 is not a factor of 37.
\ng) Yes, 15 is a factor of 75.
\nh) Yes, 12 is a factor of 75.<\/p>\n

Question 3.
\nWhat are the factors of 66 ?
\nAnswer:
\nFactors of 66 = 1 \u00d7 66
\n= 2 \u00d7 33
\n= 3 \u00d7 22
\n= 6 \u00d7 11
\nFactors are 1, 2, 3, 6, 11, 22, 33 and 66.<\/p>\n

\"AP<\/p>\n

Question 4.
\nWrite all the even factors of 64.
\nAnswer:
\nFactors of 64 = 1 \u00d7 64 = 2 \u00d7 32
\n= 4 \u00d7 16 = 8 \u00d7 8
\nEven Factors of 64 are : 2, 4, 8, 16, 32 and 64.<\/p>\n

Question 5.
\nList out the numbers, which are prime \/ composite below 20.
\nAnswer:<\/p>\n

\"AP<\/p>\n

Fun activity:<\/p>\n

\"AP<\/p>\n

Answer the following questions:<\/p>\n

Question 1.
\nWhat are the prime numbers between 1 to 10 ?
\nAnswer:
\n2, 3, 5, 7.<\/p>\n

Question 2.
\nWhat are the prime numbers between 10 to 20 ?
\nAnswer:
\n11, 13, 17, 19.<\/p>\n

\"AP<\/p>\n

Question 3.
\nWhat are the prime numbers between 20 to 50 ?
\nAnswer:
\n23, 29, 31, 37, 41, 43, 47.<\/p>\n

Question 4.
\nHow many prime numbers are there between 1 to 50 ?
\nAnswer:
\n15 prime numbers are there. (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 49).<\/p>\n

Question 5.
\nWhat are the prime numbers between 50 to 100 ?
\nAnswer:
\n53, 59, 61, 67, 71, 73, 79, 83, 87, 89, 97.<\/p>\n

Question 6.
\nHow many prime numbers are there between 50 to 100 ?
\nAnswer:
\n10 prime numbers are there between 50 to 100.<\/p>\n

Question 7.
\nDo you observe any speciality in these prime numbers ? What is it ?
\nAnswer:
\nAll numbers are odd, ‘2’ is only one even prime.<\/p>\n

Question 8.
\nAre the all prime numbers even or odd ?
\nAnswer:
\nAll are odd except 2.<\/p>\n

\"AP<\/p>\n

Do these: (TextBook Page No.78)<\/span><\/p>\n

a) 52
\nb) 100
\nc) 88
\nd) 96
\ne) 90
\nAnswer:
\na) \"AP<\/p>\n

\u2234 Prime factorisation of 52 = 2 \u00d7 2 \u00d7 13<\/p>\n

b) \"AP<\/p>\n

\u2234 Prime factorisation of 100 = 2 \u00d7 2 \u00d7 5 \u00d7 5<\/p>\n

c) \"AP<\/p>\n

\u2234 Prime factorisation of 88 = 2 \u00d7 2 \u00d7 2 \u00d7 11<\/p>\n

\"AP<\/p>\n

d) \"AP<\/p>\n

\u2234 Prime factorisation of 96 = 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 3<\/p>\n

e) \"AP<\/p>\n

\u2234 Prime factorisation of 90 = 2 \u00d7 3 \u00d7 3 \u00d7 5<\/p>\n

Question 2.
\nThe prime factorisation of 12 \u00d7 15 is
\nAnswer:<\/p>\n

\"AP<\/p>\n

\u2234 12 \u00d7 15 = 2 \u00d7 2 \u00d7 3 \u00d7 3 \u00d7 5.<\/p>\n

\"AP<\/p>\n

Question 3.
\nMatch the following:<\/p>\n

\"AP<\/p>\n

Answer:<\/p>\n

\"AP<\/p>\n

Question 4.
\n5 \u00d7 2 \u00d7 3 \u00d7 3 is the prime factorisation of _________
\nAnswer:
\n90<\/p>\n

Do this: (TextBook Page No.79)<\/span><\/p>\n

Question 1.
\nFind the common factors of the following numbers and represent in the diagram.
\na) 6 and 12
\nb) 12 and 20
\nc) 9 and 18
\nd) 11 and 22
\nAnswer:
\na) Factors of 6 = 1, 2, 3, 6
\nFactors of 12 = 1, 2, 3, 4, 6, 12<\/p>\n

\"AP<\/p>\n

b) Factors of 12 = 1, 2, 3, 4, 6, 12
\nFactors of 20 = 1, 2, 4, 5, 10, 20<\/p>\n

\"AP<\/p>\n

c) Factors of 9 = 1, 3, 9
\nFactors of 18 = 1, 2, 3, 6, 9, 18<\/p>\n

\"AP<\/p>\n

d) Factors of 11 = 1, 11
\nFactors of 22 = 1,2, 11, 22<\/p>\n

\"AP<\/p>\n

\"AP<\/p>\n

Do this: (TextBook Page No.80)<\/span><\/p>\n

Find the HCF of the following pairs of numbers by writing common factors.
\n1) 21 and 28
\n2) 34 and 20
\n3) 33 and 39
\n4) 16 and 36
\n5) 12 and 18
\n6) 80 and loo
\nAnswer:
\n1) Factors of 21 = 1, 3, 7, 21
\nFactors of 28 = 1, 2, 4, 7, 14, 28
\nCommon factors of 21 and 28 = 1, 7
\nHCF of 21 and 28 = 7.<\/p>\n

2) Factors of 34 = 1, 2, 17, 34
\nFactors of 20 = 1, 2, 4, 5, 10, 20
\nCommon factors of 34 and 20 = 1, 2
\nHCF of 34 and 20 = 1, 2.<\/p>\n

3) Factors of 33 = 1, 3, 11, 33
\nFactors of 39 = 1, 3, 13, 39
\nCommon factors of 33 and 39 = 1, 3
\nHCF of 33 and 39 = 3.<\/p>\n

4) Factors of 16 = 1, 2, 4, 8, 16
\nFactors of 36 = 1, 2, 3, 4, 9, 12, 18, 36
\nCommon factors of 16 and 36 = 1, 2, 4<\/p>\n

5) Factors of 12 = 1, 2, 3, 4, 6, 12
\nFactors of 18 = 1, 2, 3, 6, 9, 18
\nCommon factors of 12 and 18 = 1,2, 3, 6
\nHCF of 12 and 18 = 6<\/p>\n

6) Factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
\nFactors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100
\nCommon factors of 80 and 100 = 1, 2, 4, 5, 10, 20
\nHCF of 80 and 100 = 20.<\/p>\n

\"AP<\/p>\n

Try this: (TextBook Page No.80)<\/span><\/p>\n

Find the HCF for the following pair of numbers. What do you observe ?
\n1) 4, 16
\n2) 4, 12
\n3) 5, 15
\n4) 14, 42
\nAnswer:
\n1) Factors of 4 = 1, 2, 4
\nFactors of 16 = 1,2, 4, 8, 16
\nCommon factors of 4 and 16 = 1, 2, 4
\nHCF of 4 and 16 = 4.<\/p>\n

2) Factors of 4 = 1, 2, 4
\nFactors of 12 = 1,2, 3, 4, 6, 12
\nCommon factors of 4 and 12 = 1, 2, 4
\nHCF of 4 and 12 = 4.<\/p>\n

3) Factors of 5 = 1, 5
\nFactors of 15 = 1, 3, 5, 15
\nCommon factors of 5 and 15 = 1, 5
\nHCF of 5 and 15 = 5.<\/p>\n

4) Factors of 14 = 1, 2, 7
\nFactors of 42 = 1, 2, 3, 6, 7, 14, 21, 22
\nCommon factors of 14 and 42 = 1, 2, 7
\nHCF of 14 and 42 = 7<\/p>\n

Observation :
\nIn pair of numbers, if one of them is multiple of the other. The smallest number is the HCF of the pair of number.<\/p>\n

\"AP<\/p>\n

Do these: (TextBook Page 82)<\/span><\/p>\n

Question 1.
\nFind LCM and HCF by prime factorisation method for the following.
\na) 15, 48
\nb) 18, 42, 48
\nc) 15, 25, 30
\nd) 10, 15, 25
\ne) 15, 18, 36, 20
\nAnswer:
\na) Given numbers 15 and 48.<\/p>\n

\"AP<\/p>\n

Prime factorisation of 15 = 1 \u00d7 3 \u00d7 5
\nPrime factorisation of 48 = 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 3
\nCommon factors = 1 \u00d7 3
\nOther factors = 5 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2
\nLCM = 1 \u00d7 3 \u00d7 5 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 = 240
\nHCF = 1 \u00d7 3 = 3.<\/p>\n

\"AP<\/p>\n

b) Given numbers 18, 42 and 48.<\/p>\n

\"AP<\/p>\n

Prime factorisation of 18 = 1 \u00d7 2 \u00d7 3 \u00d7 3
\nPrime factorisation of 42 = 1 \u00d7 2 \u00d7 3 \u00d7 7
\nCommon factors = 1 \u00d7 2 \u00d7 3
\nOther factors = 3 \u00d7 7 \u00d7 2 \u00d7 2 \u00d7 2
\nLCM = 1 \u00d7 2 \u00d7 3 \u00d7 3 \u00d7 7 \u00d7 2 \u00d7 2 \u00d7 2 = 1008
\nHCF = 1 \u00d7 2 \u00d7 3 = 6<\/p>\n

c) Given numbers 15, 25 and 30<\/p>\n

\"AP<\/p>\n

Prime factorisation of 15 = 1 \u00d7 3 \u00d7 5
\nPrime factorisation of 25 = 1 \u00d7 5 \u00d7 5
\nPrime factorisation of 30 = 1 \u00d7 2 \u00d7 3 \u00d7 5
\nCommon factors = 1 \u00d7 5
\nOther factors = 3 \u00d7 3 \u00d7 5 \u00d7 2
\nLCM = 1 \u00d7 5 \u00d7 3 \u00d7 3 \u00d7 5 \u00d7 2 = 450
\nHCF = 1 \u00d7 5 = 5.<\/p>\n

\"AP<\/p>\n

d) Given numbers 10, 15 and 25<\/p>\n

\"AP<\/p>\n

Prime factorisation of 10 = 1 \u00d7 2 \u00d7 5
\nPrime factorisation of 15 = 1 \u00d7 3 \u00d7 5
\nPrime factorisation of 25 = 1 \u00d7 5 \u00d7 5
\nCommon factors = 1 \u00d7 5 = 5
\nOther factors = 2 \u00d7 3 \u00d7 5 = 30
\nLCM = 5 \u00d7 30 = 150
\nHCF = 5<\/p>\n

e) Given numbers 15, 18, 36 and 20<\/p>\n

\"AP<\/p>\n

Prime factorisation of 15 = 1 \u00d7 3 \u00d7 5
\nPrime factorisation of 18 = 1 \u00d7 2 \u00d7 3 \u00d7 3
\nPrime factorisation of 36 = 1 \u00d7 3 \u00d7 3 \u00d7 2 \u00d7 2
\nPrime factorisation of 20 = 1 \u00d7 2 \u00d7 2 \u00d7 5
\nCommon factors = 1
\nOther factors = 3 \u00d7 5 \u00d7 2 \u00d7 3 \u00d7 3 \u00d7 3 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 5 = 194,400
\nLCM = 194, 400
\nHCF = 1.<\/p>\n

\"AP<\/p>\n

Question 2.
\nFind LCM and HCF by division method.
\na) 16, 28, 36
\nb) 12, 18, 42
\nc) 30, 75, 90
\nd) 24, 32, 48
\ne) 12, 15, 18<\/p>\n

Answer:
\na) Given numbers 16, 28 and 36<\/p>\n

\"AP<\/p>\n

LCM = 2 \u00d7 2 \u00d7 4 \u00d7 7 \u00d7 9 = 1008
\nHCF = 2 \u00d7 2 = 4<\/p>\n

b) Given numbers 12, 18 and 42<\/p>\n

\"AP<\/p>\n

LCM = 2 \u00d7 3 \u00d7 2 \u00d7 3 \u00d7 7 = 252
\nHCF = 2 \u00d7 3 = 6<\/p>\n

c) Given numbers 30, 75, 90<\/p>\n

\"AP<\/p>\n

LCM = 5 \u00d7 3 \u00d7 2 \u00d7 5 x 6
\nHCF = 5 \u00d7 3 = 15<\/p>\n

d) Given numbers 24, 32, 48<\/p>\n

\"AP<\/p>\n

LCM = 4 \u00d7 2 \u00d7 3 \u00d7 4 \u00d7 6 = 576
\nHCF = 4 \u00d7 2 = 8<\/p>\n

e) Given numbers 12, 15 and 18<\/p>\n

\"AP<\/p>\n

LCM = 3 \u00d7 2 \u00d7 2 \u00d7 5 \u00d7 6 = 360
\nHCF = 3<\/p>\n

\"AP<\/p>\n

Exercise 3:<\/span><\/p>\n

Solve the following word-problems:<\/p>\n

Question 1.
\nThere are some fruits in a basket. If we arrange 4 or 6 or 8 or 10 fruits in a pile, no fruits are left in the bas\u00acket. What is the minimum number of fruits in the basket ?<\/p>\n

\"AP<\/p>\n

Answer:
\nArrangement of fruits in a pile are 4 or 6 or 8 or 10
\nWe need to find the LCM of 4, 6, 8, 10<\/p>\n

\"AP<\/p>\n

LCM = 2 \u00d7 2 \u00d7 1 \u00d7 3 \u00d7 2 \u00d7 5 = 120
\nThe minimum number of fruits in the basket = 120.<\/p>\n

Question 2.
\nRamu has 16 blue marbles and 12 white ones. If he wants to arrange them in identical groups without leaving any marbles, what is the maximum number in each group Ramu can make?<\/p>\n

\"AP<\/p>\n

Answer:
\nNumber of marbles Ramu has = 16 and 12
\nWe need to find the HCF of 12 and 16<\/p>\n

\"AP<\/p>\n

HCF = 4
\nMaximum number of marbles Ramu can make = 4.<\/p>\n

\"AP<\/p>\n

Question 3.
\nTwo Neon lights are turned on at the same time. One blinks for every 4 seconds and other blinks for every 6 seconds. In 60 seconds how many times will they blink at a time ?<\/p>\n

\"AP<\/p>\n

Answer:
\nBlink time of lights = 4 sec and 6 sec
\nLCM of 4 and 6 = \"AP
\nLCM = 2 \u00d7 2 \u00d7 3 = 12 sec
\nThe lights blinks at a time for every 12 sec.
\nGiven time = 60 sec
\nNumber of times will the lights blink = 60 \u00f7 12 = 5 times.<\/p>\n

Question 4.
\nThere are 40 girls and 32 boys, who want to participate in state-level games competition. If each team must have the same number of girls and the same number of boys.
\ni) What is the maximum number in each team that can participate in state-level games ?
\nii) How many boys and girls will be on each team?<\/p>\n

\"AP<\/p>\n

Answer:
\nNumber of boys 32 and girls participate in the game is 32 and 40
\ni) To find maximum number in each team can participate in state-level game, we need to find
\nHCF of 32 and 40<\/p>\n

\"AP<\/p>\n

\u2234 HCF = 2 \u00d7 2 \u00d7 2 = 8
\nThe maximum number in each team = 8 numbers.<\/p>\n

ii) To find out boys and girls will be an each team, we find LCM of 32 and 40.<\/p>\n

\"AP<\/p>\n

\u2234 LCM of 32 and 40 = 2 \u00d7 2 \u00d7 2 \u00d7 4 \u00d7 5 = 160.<\/p>\n

Question 5.
\nFind the least number of sheets of paper required to make notebooks containing 32 sheets or 40 sheets or 48 sheets without a single sheet leaving behind.<\/p>\n

\"AP<\/p>\n

Answer:
\nTo find the least number of sheets of paper required to make note books, we need to find LCM of 32, 40, 48.<\/p>\n

\"AP<\/p>\n

LCM = 2 \u00d7 2 \u00d7 2 \u00d7 4 \u00d7 5 \u00d7 6 = 960
\n\u2234 960 of sheets of paper required to make notebooks containing given sheets.<\/p>\n

\"AP<\/p>\n

Question 6.
\nWhat is the least number of chairs needed for an auditorium so that they can be arranged either 27 in a row or 33 in a row?<\/p>\n

\"AP<\/p>\n

Answer:
\nTo find least number of chairs needed for an auditorium are need to find LCM of 27 and 33.<\/p>\n

\"AP<\/p>\n

LCM = 3 \u00d7 9 \u00d7 11 = 297.
\n\u2234 297 chairs needed for an auditorium.<\/p>\n","protected":false},"excerpt":{"rendered":"

Andhra Pradesh AP Board 5th Class Maths Solutions 5th Lesson Multiples and Factors World Textbook Exercise Questions and Answers. AP State Syllabus 5th Class Maths Solutions Chapter 5 Multiples and Factors Question 1. Observe which numbers are not divisible? Answer: Which of the above numbers are exactly divisible by 2? Answer: 2410, 1282, 3784, 6728, … Read more<\/a><\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[16],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/24450"}],"collection":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/comments?post=24450"}],"version-history":[{"count":4,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/24450\/revisions"}],"predecessor-version":[{"id":24503,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/24450\/revisions\/24503"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/media?parent=24450"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/categories?post=24450"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/tags?post=24450"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}