Question

Find the greatest number , which divides 101 and 77, laeving a reminder of 5 in both case?

Answer 1

3 is the greatest number which divides 101 and 77 leaving a reminder of 5 in both case

Answer 2

The greatest number which divides 101 and 77 leaving a reminder of 5 in both case is 12.

Given:-

The two numbers = 101 and 77

Reminder in each case = 5

To Find:-

The greatest number which divides 101 and 77 leaving a reminder of 5 in both case.

Solution:-

We can easily find out the value of the greatest number which divides 101 and 77 leaving a reminder of 5 in both case by using these simple steps.

As

The two numbers = 101 and 77

Reminder in each case = 5

Now, original numbers = 101 - 5 = 96

77 -5 = 72

For finding the greatest number, we need to find the prime factors of both these numbers.

96 = 3 × 2 × 2 × 2 × 2 × 2

72 = 3 × 3 × 2 × 2 × 2

So, the common factors between 96 and 72 are = 3 × 2 × 2 = 12

Hence, The greatest number which divides 101 and 77 leaving a reminder of 5 in both case is 12.

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