Question

1. Find the HCF of the following numbers by prime factorisation and short division method. a. 28, 42 e. 25, 35, 55 i. 70, 105, 35 b. 36,96 f. 21, 49, 63 j. 34, 26,58 c. 24, 48, 72 g. 16, 48, 80 d. 16, 36,56 h. 32, 120, 64 1. 125, 100 k. 18, 27,54

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Answer 1

a. 28, 42 is the highest common factor is 14.

b. 36, 96 is the highest common factor is 12.

c. 24, 48, 72 is the highest  common factor is 24.

d. 16, 36,56 is the highest common factor is 4.

e. 25, 35, 55 is the highest common factor is 5.

f. 21, 49, 63 is the highest common factor is 7.

g. 16, 48, 80 is the highest common factor is 16.

h. 32, 120, 64 is the highest common factor is 8.

i. 70, 105, 35 is the highest common factor is 35.

j. 34, 26, 58 is the highest common factor is 2.

k. 18, 27, 54 is the highest common factor is 9.

Given that,

We have to find the HCF of the number

a. 28, 42

The factors of 28 are: 1, 2,4, 7, 14, 28

The factors of 42 are: 1, 2,3, 6,7,14, 21, 42

Then the greatest common factor is 14. [ HCF is also know as GCF]

b. 36, 96

The factors of 36 are: 1, 2,3, 4,6, 9, 12, 18,36

The factors of 96 are: 1, 2,3, 4,6, 8, 12, 16,24, 32, 48, 96

Then the highest common factor is 12.

c. 24, 48, 72

The factors of 24 are: 1, 2,3, 4, 6, 8, 12, 24

The factors of 48 are: 1, 2,3, 4, 6, 8, 12, 16, 24, 48

The factors of 72 are: 1, 2,3, 4, 6, 8, 9, 12, 18, 24, 36, 72

Then the highest  common factor is 24.

d. 16, 36,56

The factors of 16 are: 1, 2,4, 8,16

The factors of 36 are: 1, 2,3, 4,6, 9, 12,18, 36

The factors of 56 are: 1, 2,4, 7, 8, 14, 28, 56

Then the highest common factor is 4.

e. 25, 35, 55

The factors of 25 are: 1, 5,25

The factors of 35 are: 1, 5,7, 35

The factors of 55 are: 1, 5,11,55

Then the highest common factor is 5.

f. 21, 49, 63

The factors of 21 are: 1, 3,7,21

The factors of 49 are: 1, 7,49

The factors of 63 are: 1, 3,7,9, 21,63

Then the highest common factor is 7.

g. 16, 48, 80

The factors of 16 are: 1, 2, 4,8, 16

The factors of 48 are: 1, 2, 3,4, 6, 8,12, 16, 24, 48

The factors of 80 are: 1, 2, 4,5, 8, 10,16, 20, 40, 80

Then the highest common factor is 16.

h. 32, 120, 64

The factors of 32 are: 1, 2,4,8, 16, 32

The factors of 64 are: 1, 2, 4,8, 16, 32, 64

The factors of 120 are: 1, 2,3,4, 5, 6, 8, 10, 12, 15, 20, 24, 30,40, 60, 120

Then the highest common factor is 8.

i. 70, 105, 35

The factors of 35 are: 1, 5, 7,35

The factors of 70 are: 1, 2, 5,7,10, 14, 35, 70

The factors of 105 are: 1, 3, 5,7, 15, 21, 35, 105

Then the highest common factor is 35.

j. 34, 26,58

The factors of 26 are: 1,2,13, 26

The factors of 34 are: 1, 2,17, 34

The factors of 58 are: 1,2,29, 58

Then the highest common factor is 2.

k. 18, 27, 54

The factors of 18 are: 1, 2,3,6, 9,18

The factors of 27 are: 1, 3,9,27

The factors of 54 are: 1, 2,3,6, 9,18, 27, 54

Therefore, the highest common factor is 9.

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