Correct option is A)

Clearly, the required number is the HC.F of the numbers

626−1=625,3127−2=3125 and 15628−3=15625.

Using Euclid's division lemma to find the H.C.F. of 625 and 3125.

3125=625 × 5+0

Clearly, H.C.F. of 625 and 3125 is 625.

Now, H.C.F. of 625 and 15625

15625=625 × 25+0

So, the H.C.F of 625 and 15625 is 625

Hence, H.C.F of 625,3125 and 15625 is 625.

Hence, the required number is 625.