Question

find the largest number which divides 546 $ 764 leaving remainder 6 8 respectively.

Answer 1

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

Answer 2

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