If the highest common factor of numbers 408 and 1032 is expressed in the form of 1032x – 408 × 5, then find the value of x.

Question

Philoid · Accepted Answer

If the HCF of 408 and 1032 can be written as

By Euclid’s division algorithm,

1032 = 408×2 + 216

408 = 216×1 + 192

216 = 192×1 + 24

192 = 24×8 + 0

Since the remainder becomes 0 here, so HCF of 408 and 1032 is 24

Now,

1032x - 408*5 = HCF of these numbers

⟹ 1032x - 2040 = 24

⟹ 1032x = 24 + 2040

⟹ x = 2064/1032

⟹ x = 2

So value of x is 2.