Question

find the h.c.f of the following by prime factor method: a) 22,44. b)54,72. c)27,64. d)36,30,35. e)21,28,49 ​

Answer 1

Answer:

a) 22=2×11×1

44=2×2×11×1

b) 54=2×27×1

72=2×2×2×3×3×1

c) 27=27×1

64=2×2×2×2×2×2×1

d) 36= 2×2×3×3×1

30 = 2×3×5×1

35=5×7×1

e) 21=7×3×1

28=2×2×7×1

49=7×7×1

Answer 2

Finding the HCF of the numbers by prime factorization,

• [Hint: To find HCF, choose the common and select the lowest power of the common.]

(a) 22, 44

22 = 2 × 11

44 = 2 × 2 × 11 = 2² × 11

HCF(22, 44) = 2 × 11 = 22

(b) 54, 72

54 = 2 × 3 × 3 × 3 = 2 × 3³

72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3²

HCF(54, 72) = 2 × 3² = 2 × 9 = 18

(c) 27, 64

27 = 3 × 3 × 3 = 3³

64 = 2 × 2 × 2 × 2 × 2 × 2 = 2⁸

HCF(27, 64) = 1

(d)36, 30, 35

36 = 2 × 2 × 3 × 3 = 2² × 3²

30 = 2 × 3 × 5

35 = 5 × 7

HCF(36, 30, 35) = 1

(e)21, 28, 49

21 = 3 × 7

28 = 2 × 2 × 7 = 2² × 7

49 = 7 × 7

HCF(21, 28, 49) = 7