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

2
by piggyyyyyy

2015-01-27T00:24:07+05:30

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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
2015-01-27T12:48:12+05:30
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