Question

Find the largest number which divides 129 and 545 , leaving remainders 3 and 5 respectively.

Answer 1

To find the largest number which divides 129 and 545 leaving remainder 3 and 5 i.e. HCF.

Consider HCF be x.

In order to make 129 and 545 completely divisible by x, we need to deduct the remainder 3 and 5 from the cases.

126 =2× 3 x 3 x 7

540= 2×2×3×3 x 3 x 5

⇒ x = 2×3×3 = 18

∴ largest number which divides 129 and 545 leaving remainder 3 and 5 in case is 18.