Question

Find the greatest number that will divide 508, 635, and 762 leaving reamainder 4, 5and 6 respectively

Answer 1

Subtract 4 , 5 and 6 respectively from 508, 635 and 762 we get the number 504, 630 and 756.

Let a = 630 and b = 504

Euclid division algorithm

630 = 504 × 1 + 126

504 = 126 × 4 + 0

HCF (630,504) = 126

Find HCF of 756 and 126

756 = 126 × 6 + 0

HCF (756,126) = 126

Thus

HCF of 504, 630 and 756 = 126

Hence the number is 126

Answer 2

Subtract :-

508 - 4 = 504

635 - 5 = 630

762 - 6 = 756

Let a = 630 and b = 504

We have Euclid division algorithm :-

630 = 504 × 1 + 126

504 = 126 × 4 + 0

HCF of (630,504) = 126

Now :-

HCF of 756 and 126

756 = 126 × 6 + 0

HCF (756,126) = 126

So

HCF of 504 ,630 and 756 = 126

Answer = 126