Practice the questions given in the worksheet on hcf (highest common factor) by factorization method, prime factorization method and division method.

I. Find the common factors of the following numbers.

(i) 6 and 8

(ii) 9 and 15

(iii) 16 and 18

(iv) 16 and 28

(v) 51 and 68

(vi) 27 and 45

II. Which pairs are co-prime?

(i) 16, 18

(ii) 15, 14

(iii) 27, 28

(iv) 8, 15

(v) 11, 12

(vi) 45, 49

III. Find the H.C.F. of the following by prime factorization method.

(i) 56, 72

(ii) 21, 35

(iii) 56, 70

(iv) 45, 81

(v) 42, 49

(vi) 44, 66, 110

IV. Find the H.C.F. of the following by factorization method.

(i) 16, 24

(ii) 28, 35

(iii) 48, 60

(iv) 15, 52, 65

(v) 15, 18, 30

(vi) 42, 54, 64

V. Find the H.C.F. of the following by division method.

(i) 8, 16 and 36

(ii) 9, 18 and 27

(iii) 20, 80 and 128

(iv) 60, 80, 90

(v) 25, 75, 95

(vi) 12, 24, 88

VI. Solve the following.

(i) Two ropes are 64 cm and 80 cm long. What maximum length of pieces can be cutequally from the given ropes?

(ii) Find the greatest number which divides 8, 18 and 24 exactly.

(iii) Find the greatest number which is less by 1 to divide 15, 18 and 30 exactly.

(iv) Find the greatest number which is more by 5 to divide 12, 24 and 60 exactly.

(v) Find the greatest number which is less by 2 to divide 18, 36 and 45 exactly.

(vi) Find the greatest number which is more by 7 to divide 184, 230 and 276 exactly.

Answers for the worksheet on hcf are given below.

**Answers:**

I. (i) 2

(ii) 3

(iii) 2

(iv) 2, 4

(v) 17

(vi) 3, 9

II. (ii) 15, 14

(iii) 27, 28

(iv) 8, 15

(v) 11, 12

(vi) 45, 49

III. (i) 8

(ii) 7

(iii) 14

(iv) 9

(v) 7

(vi) 22

IV. (i) 8

(ii) 7

(iii) 12

(iv) 1

(v) 3

(vi) 2

V. (i) 4

(ii) 9

(iii) 4

(iv) 10

(v) 5

(vi) 4

VI. (i) 16 cm

(ii) 2

(iii) 2

(iv) 17

(v) 7

(vi) 53

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