Question

Find the greatest number which divides 87 and 97 leaving remainder 7 in each case.

Answer 1

As we know that the greatest number which divides two or more numbers is known as their HCF.

Here we find the greatest no. which divides 87 and 97 leaving 7 as remainder.

first of all subtract 7 from both these numbers and then calculate the HCF of resultant numbers . we will get our answer.

So , 87 - 7 = 80 and 97 - 7 = 90

Here, 80 = 2×2×2×2×5

and 90 = 2×3×3×5

2 and 5 are common factors of 80 and 90. Therefore HCF of 80 and 90 is 2×5

HCF (80 , 90) = 10

Thus 10 is the greatest number which divides 87 and 97 leaving 7 as remainder.