Greatest Common Factor of 117 and 135

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 117, 135 i.e. 9 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 117 and 135 is 9.

GCF(117,135) = 9

GCF of 117 and 135

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

GCF of:
and

Greatest Common Factor of 117 and 135

GCF of 117 and 135 is 9

Prime Factorization of 117


3 117
3 39
13 13
1

Prime factors of 117 are 3,13. Prime factorization of 117 in exponential form is:

117 = 32×131

Prime Factorization of 135


3 135
3 45
3 15
5 5
1

Prime factors of 135 are 3,5. Prime factorization of 135 in exponential form is:

135 = 33×51

∴ So by taking common prime factors GCF of 117 and 135 is 9

Greatest Common Factor of 117 and 135 by matching factors method

Factors of 117

List of positive integer factors of 117 that divides 117 without a remainder.

1,3,9,13,39,117

Factors of 135

List of positive integer factors of 135 that divides 135 without a remainder.

1,3,5,9,15,27,45,135

Greatest Common Factor

We found the factors and prime factorization of 117 and 135. The biggest common factor number is the GCF number.
So the greatest common factor 117 and 135 is 9.

Also check out the Least Common Multiple of 117 and 135

Properties of GCF 117 and 135

(i) The GCF of 117 and 135 is associative

GCF of 117 and 135 = GCF of 135 and 117

Related Greatest Common Factor of 117

Related Greatest Common Factor of 135

Frequently Asked Questions on GCF of 117 and 135

1. What is the GCF of 117 and 135?

Answer: GCF of 117 and 135 is 9.

2. What are the Factors of 117?

Answer: Factors of 117 are 1, 3, 9, 13, 39, 117. There are 6 integers that are factors of 117. The greatest factor of 117 is 117.

3. What are the Factors of 135?

Answer: Factors of 135 are 1, 3, 5, 9, 15, 27, 45, 135. There are 8 integers that are factors of 135. The greatest factor of 135 is 135.

4. How to Find the GCF of 117 and 135?

Answer:

Greatest Common Factor of 117 and 135 = 9

Step 1: Find the prime factorization of 117

117 = 3 x 3 x 13

Step 2: Find the prime factorization of 135

135 = 3 x 3 x 3 x 5

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 3 x 3 = 9

Step 4: Therefore, the greatest common factor of 117 and 135 is 9