Question

Find the HCF of 1008 and 1080 by prime factorisation method.

Answer 1

Given: HCF(1008, 1080)

Step-wise calculation:

1. Prime factors of 1008:

1008 = 2 × 504

= 2² × 252 

= 2³ × 126

= 2⁴ × 63

= 2⁴ × 3² × 7 

⇒ 1008 = 2⁴ × 3² × 7

2. Prime factors of 1080:

1080 = 2 × 540

= 2² × 270

= 2³ × 135

= 2³ × 3³ × 5

⇒ 1080 = 2³ × 3³ × 5

3. Take common primes with the smallest exponents:

Common primes: 2 and 3

Smallest powers: `2^(min(4,  3)) = 2^3` 

`3^(min(2,  3)) = 3^2` 

HCF = 2³ × 3² 

= 8 × 9 

= 72

HCF(1008, 1080) = 72.