Question

Find the largest number which divides 546 and 764, leaving remainders 6 and 8 respectively.

Answer 1

Given: Numbers 546 and 764 leave remainders 6 and 8 respectively.

Subtract the remainders: 546 – 6 = 540 and 764 – 8 = 756.

The required largest divisor is the HCF (gcd) of 540 and 756.

Compute gcd(540, 756) by the Euclidean algorithm: 

756 = 540 × 1 + 216

540 = 216 × 2 + 108

216 = 108 × 2 + 0

So, gcd = 108.

The largest number is 108.