If the H.C.F of 408 and 1032 is expressible in the form 1032 m – 408 × 5. Find m.

First we will find out the H.C.F of 408 and 1032 by using Euclid division lemma

1032 = 408 × 2 + 216

408 = 216 × 1 + 192

216 = 192 × 1 + 24

192 = 24 × 8 +0

Now since the remainder is zero

The H.C.F is 24

Given that the H.C.F 408 and 1032 can be expressed as = 1032 m – 408 × 5

⇒ 1032 m – 408 × 5 = 24

⇒ 1032 m – 2040 = 24

⇒ 1032m = 24 + 2040

⇒ 1032m = 2064

⇒ m = 2