Question

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

Answer 1

We know the required number divides 540 (546 − 6) and 756 (764 − 8), respectively.
∴ Required largest number = HCF (540, 756)
Prime factorisation:
540 = $2\times 2\times 3\times 3\times 3\times 5=2^2\times 3^2\times 5$
756 = $2\times 2\times 3\times 3\times 3\times 7=2^2\times 3^3\times 7$
∴ HCF = $2^2\times 3^3=108$
Hence, the largest number is 108.