Question

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

Answer 1

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 = \(\frac{2064}{1032}\) ⇒ 2

Therefore m = 2