Greatest Common Factor of 114 and 117

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 114, 117 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 114 and 117 is 3.

GCF(114,117) = 3

GCF of 114 and 117

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

GCF of:
and

Greatest Common Factor of 114 and 117

GCF of 114 and 117 is 3

Prime Factorization of 114


2 114
3 57
19 19
1

Prime factors of 114 are 2,3,19. Prime factorization of 114 in exponential form is:

114 = 21×31×191

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

∴ So by taking common prime factors GCF of 114 and 117 is 3

Greatest Common Factor of 114 and 117 by matching factors method

Factors of 114

List of positive integer factors of 114 that divides 114 without a remainder.

1,2,3,6,19,38,57,114

Factors of 117

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

1,3,9,13,39,117

Greatest Common Factor

We found the factors and prime factorization of 114 and 117. The biggest common factor number is the GCF number.
So the greatest common factor 114 and 117 is 3.

Also check out the Least Common Multiple of 114 and 117

Properties of GCF 114 and 117

(i) The GCF of 114 and 117 is associative

GCF of 114 and 117 = GCF of 117 and 114

Related Greatest Common Factor of 114

Related Greatest Common Factor of 117

Frequently Asked Questions on GCF of 114 and 117

1. What is the GCF of 114 and 117?

Answer: GCF of 114 and 117 is 3.

2. What are the Factors of 114?

Answer: Factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114. There are 8 integers that are factors of 114. The greatest factor of 114 is 114.

3. 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.

4. How to Find the GCF of 114 and 117?

Answer:

Greatest Common Factor of 114 and 117 = 3

Step 1: Find the prime factorization of 114

114 = 2 x 3 x 19

Step 2: Find the prime factorization of 117

117 = 3 x 3 x 13

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

GCF = 3

Step 4: Therefore, the greatest common factor of 114 and 117 is 3