Question

find the greatest number which on dividing 1661 and 2045, leaves a reminder of 10 and 13 respectively?

Answer 1

Let the greatest number is x.

If x divides 1661 then 10 is remainder and when x divides 2045 then remainder is 13.

So evaluate the HCF of 1661-10 = 1651 and 2045-13 = 2032

1651 = 13×127

2032 = 2×2×2×2×127

Hence HCF ( 1651, 2032) = 127

Hence the greatest number is 127.