Question

The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is:​

Answer 1

Answer:

Hence, HCF(1651, 2032) = 127. Hence, the greatest number which divides 1657 and 2037 leaves a remainder of 6 and 5 respectively is 127.

Answer 2

Answer:

Complete step-by-step answer:

We have with us, the two numbers which are: 1657 and 2037.

When we divide these numbers by the required number, we have the remainders of 6 and 5 respectively.

So, let us first just remove these remainders to get a clean and perfect division.

Now, we will have: 1657 – 6 = 1651

And 2037 – 5 = 2032.

Now, we have created two new numbers 1651 and 2032 which are perfectly divisible by the number we are required to find.

If two numbers are divisible by some number that means that number is a factor of both the numbers.

The number is given to be greatest.

Hence, we just need to find HCF.

So, let us first do the prime factorization of

1651=13×127 and 2032=2×2×2×2×127.

We see that they only have 127 common in their prime factorization.

Hence, HCF(1651, 2032) = 127.

Hence, the greatest number which divides 1657 and 2037 leaves a remainder of 6 and 5 respectively is 127.

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