Find the greatest perfect square that is a factor of the number 117

Given number is 117.

We know about perfect square numbers, all the perfect squares below 117 are :- 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

We need to check the divisibility of 117 by these perfect squares written above.

117 is divisible by 1.

117 is an odd number, so it is not divisible by 4.

To check divisibility by 9, the sum of digits of number must be divisible by 9. So 1 + 1 + 7 = 9, it means 117 is divisible by 9.

The factors of 117 would be :- 117 = 9 × 13.

We know 13 is a prime number, so we can not factor it anymore.

It means 9 is the greatest perfect square that is factor of 117.

Hence, 9 is the final answer.

answer

step-by-step explanation: