Answer:

Here is your answer:

108

Step-by-step explanation:

It is given that on dividing 546 and 764 we will get the remainder 6 and 8 respectively

this means, 546 - 6 = 540

and              764 - 8 = 756

are completely divisible by the required no.

so now we will find the HCF

( You can find the hcf by Euclid's didvision lemma or by prime factorization)

540 = 2² × 3³  × 5

756  = 2²×3³×7

so the hcf or the required no. is 2 × 2 ×3×3×3 = 108

Hence , the required number is 108.