Question

Find he greatest no. Which on dividing 1657 and 2037 leaves the remainder 6 and 5 .

Answer 1

when 1657 and 2037 are divided with that number, it leaves the remainder 6 and 5

subtract the remainders:
1657 - 6 = 1651
2037-5 = 2032

Now 2032 and 1651 are divisible by that number.
1651 = 13×127
2032 = 2×2×2×2×127 = 2⁴×127

HCF(1651,2032) = 127

So the greatest number is 127 which on dividing 1657 and 2037 leaves the remainder 6 and 5

Answer 2

When 1657 and 2037 are divided by HCF would have  remainder 6 and 5
Hence the numbers are (1657 - 6) = 1651 and (2037-5) = 2032
Now  factorizing 2032 and 1651 we have,
           2032 = 2×2×2×2×127 = 2⁴×127
           1651 = 13×127
   HCF = 127
Therefore, the greatest no. is 127 which on dividing 1657 and 2037 leaves the remainder 6 and 5