Find the largest number which divides 546 and 764,

We know the required number divides 540 (546 − 6) and 756 (764 − 8), respectively.
∴ Required largest number = HCF (540, 756)
Prime factorisation:

$540=2 \times 2 \times 3 \times 3 \times 3 \times 5=2^{2} \times 3^{2} \times 5$

$756=2 \times 2 \times 3 \times 3 \times 3 \times 7=2^{2} \times 3^{3} \times 7$

$\therefore \mathrm{HCF}=2^{2} \times 3^{3}=108$

Hence, the largest number is 108 .