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

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

Subtract the given remainders from the numbers that are given :-
626 - 1 = 625
3127 - 2 = 3125
15628 - 3 = 15625

15625 = 5 x 5 x 5 x 5 x 5 x 5
3125 = 5 x 5 x 5 x 5 x 5
625 = 5 x 5 x 5 x 5

HCF = 5 x 5 x 5 x 5 = 625

Hence, 625 is the  largest number that divides 626, 3127 and 15628 and leaves remainder of 1,2 and 3 respectively