If the HCF of 408 and 1032 is expressible in the form 1032 m – 408 × 5, find m.

Question

If the HCF of 408 and 1032 is expressible in the form 1032 m &#x2013; 408 &#xD7; 5, find m.

Philoid · Accepted Answer

Prime factors of 408: 2 × 2 × 2 x 3 × 17

Prime factors of 1032: 2 × 2 ×2 × 3 × 43

HCF of 408 and 1032 = 2 × 2 × 2 × 3 = 24

According to question:

24 = 1032 m – 408 × 5

24 = 1032 m – 2040

2064 = 1032 m

∴ m = ⇒ 2

Therefore m = 2