The factors of 117 are 1,3,9,13 and 117
117=3*3*13
To find the greatest perfect square, we must first prime factor the number and then we can look into all the factors of the number and find the greatest perfect square.
Among all the factors of 117, just 9 is a perfect square.
So, the greatest perfect square that is a factor of 117 is 9.
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.
