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Greatest Common Factor of 108 and 114

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 108, 114 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 108 and 114 is 6.

GCF(108,114) = 6

GCF of 108 and 114

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

GCF of:
and

Greatest Common Factor of 108 and 114 by Prime factorization method

Prime Factorization of 108


2 108
2 54
3 27
3 9
3 3
1

Prime factors of 108 are 2,3. Prime factorization of 108 in exponential form is:

108 = 22×33

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

∴ So by taking common prime factors GCF of 108 and 114 is 6

Greatest Common Factor of 108 and 114 by matching factors method

Factors of 108

List of positive integer factors of 108 that divides 108 without a remainder.

1,2,3,4,6,9,12,18,27,36,54,108

Factors of 114

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

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

Greatest Common Factor

We found the factors and prime factorization of 108 and 114. The biggest common factor number is the GCF number.
So the greatest common factor 108 and 114 is 6.

Also check out the Least Common Multiple of 108 and 114

Properties of GCF 108 and 114

(i) The GCF of 108 and 114 is associative

GCF of 108 and 114 = GCF of 114 and 108

Frequently Asked Questions on GCF of 108 and 114

1. What is the GCF of 108 and 114?

Answer: GCF of 108 and 114 is 6.

2. What are the Factors of 108?

Answer: Factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108. There are 12 integers that are factors of 108. The greatest factor of 108 is 108.

3. 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.

4. How to Find the GCF of 108 and 114?

Answer:

Greatest Common Factor of 108 and 114 = 6

Step 1: Find the prime factorization of 108

108 = 2 x 2 x 3 x 3 x 3

Step 2: Find the prime factorization of 114

114 = 2 x 3 x 19

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

GCF = 2 x 3 = 6

Step 4: Therefore, the greatest common factor of 108 and 114 is 6