Question

Factorize the following numbers into primes:

i. 105, 154

ii. 42, 45, 48

iii. 57, 75, 102

iv. 56, 57

v. 777, 315, 588

Answer 1

i. 105, 154

∴ 105 = 3 × 5 × 7 

154 = 2 × 2 × 11 

∴ HCF of 105 and 154 = 7

ii. 42, 45, 48

∴ 42 = 2 × 3 × 7 

45 = 3 × 3 × 5 

48 = 2 × 2 × 2 × 2 × 3 

∴ HCF of 42,45 and 48 =3

iii. 57, 75, 102

∴ 57 = 3 × 19 

75 = 3 × 5 × 5 

102 = 2 × 3 × 17 

∴ HCF of 57, 75 and 102 = 3

iv. 56, 57

∴ 56 = 2 × 2 × 2 × 7 × 1 

57 = 3 × 19 × 1 

∴ HCF of 56 and 57 = 1

v. 777, 315, 588

∴ 777 = 3 × 7 × 37 

315 = 3 × 3 × 5 × 7 

588 = 2 × 2 × 3 × 7 × 7 

∴ HCF of 777, 315 and 588 = 3 × 7 

HCF of 777, 315 and 588 = 21