Question

What is the largest number that divides 626, 3127 and 15628 and leaves remainders of 1, 2 and 3 respectively.

Answer 1

The required number when divides 626, 3127 and 15628, leaves remainder 1, 2 and 3.

This means 626 – 1 = 625, 3127 – 2 = 3125 and

15628 – 3 = 15625 are completely divisible by the number

∴ The required number = HCF of 625, 3125 and 15625

First consider 625 and 3125

By applying Euclid’s division lemma

3125 = 625 × 5 + 0

HCF of 625 and 3125 = 625

Now consider 625 and 15625

By applying Euclid’s division lemma

15625 = 625 × 25 + 0

∴ HCF of 625, 3125 and 15625 = 625

Hence required number is 625