What is the largest number that divides 626,

We need to find 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 remainders 1,2 and 3 this means $626-1=625,3127-2=3125$ and $15628-3=15625$ are completely divisible by the number.

Therefore, the required number = H.C.F. of 625, 3125 and 15625.

First we consider 625 and 3125.

By applying Euclid’s division lemma

$3125=625 \times 5+0 .$

H.C.F. of 625 and 3125 = 625

Now, consider 625 and 15625.

By applying Euclid’s division lemma

$15625=625 \times 25+0$

Therefore, H.C.F. of 625, 3125 and 15625 = 625

Hence, the required number is 625