Question

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

Answer 1

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.