Question

If the HCF of 408 and 1032-408*15 is expressible in the form 1032m-408*15 find m.

Answer 1

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.