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. Find the common factors and the highest common factor of the given numbers. One has been solved to get the idea.**

(i) 12 and 28

Factors of 12 = 1, 2, 3, 4, 6, 12

Factors of 28 = 1, 2, 4, 7, 14, 28

Common factors of 12 and 28 = 1, 2 and 4

Highest common factor (HCF) of 12 and 28 = 4

(ii) 15 and 12

(iii) 14 and 21

(iv) 18 and 24

(v) 40 and 50

**III. Which pairs are co-prime?**

(i) 16, 18

(ii) 15, 14

(iii) 27, 28

(iv) 8, 15

(v) 11, 12

(vi) 45, 49

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

(i) 24 and 36

(ii) 56 and 72

(iii) 21 and 35

(iv) 56 and 70

(v) 45 and 81

(vi) 42 and 49

(vii) 44, 66 and 110

(viii) 48, 64 and 120

(ix) 12, 15 and 18

(x) 75 and 125

(xi) 64 and 78

(xii) 27, 36 and 54

**V. 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

**VI. Find the H.C.F. of the following by Long Division Method.**

(i) 32 and 68

(ii) 45 and 180

(iii) 56 and 72

(iv) 96 and 218

(v) 8, 16 and 36

(vi) 9, 18 and 27

(vii) 20, 80 and 128

(viii) 60, 80, 90

(ix) 25, 75, 95

(x) 12, 24, 88

**VII. Find the HCF of the given numbers using venn diagram.**

(i) 14 and 16

(ii) 21 and 30

(iii) 20 and 30

(iv) 36 and 72

(v) 15 and 45

**VIII. Simplify the following using HCF.**

(i) \(\frac{25}{65}\)

(ii) \(\frac{33}{99}\)

(iii) \(\frac{20}{72}\)

(iv) \(\frac{36}{60}\)

**IX. 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) 3

(iii) 7

(iv) 6

(v) 10

**III.** (ii) 15, 14

(iii) 27, 28

(iv) 8, 15

(v) 11, 12

(vi) 45, 49

**IV.** (i) 12

(ii) 8

(iii) 7

(iv) 14

(v) 9

(vi) 7

(vii) 22

(viii) 8

(ix) 3

(x) 25

(xi) 2

(xii) 9

**V.** (i) 8

(ii) 7

(iii) 12

(iv) 1

(v) 3

(vi) 2

**VI.** (i) 4

(ii) 45

(iii) 8

(iv) 2

(v) 4

(vi) 9

(vii) 4

(viii) 10

(ix) 5

(x) 4

**VII.**

**VIII.** (i) \(\frac{5}{13}\)

(ii) \(\frac{1}{3}\)

(iii) \(\frac{5}{18}\)

(iv) \(\frac{3}{5}\)

**IX.** (i) 16 cm

(ii) 2

(iii) 2

(iv) 17

(v) 7

(vi) 53

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