Question

find the greatest number by which 1657 and 2037 are divided remainders of 6 and 5 respectively

Answer 1

Let n be the number.
If 1657 leaves remainder 6 when divided by n,
then 1651 is divisible by n.
Similarly, 2032 is divisible by n.
Now factor both numbers:
1651 = 13*127
2032 = 16*127
So the GCF of 1651 and 2032 is 127 and the answer
is 127.

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