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Greatest Common Factor of 108 and 116

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 108, 116 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 108 and 116 is 4.

GCF(108,116) = 4

GCF of 108 and 116

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

GCF of:
and

Greatest Common Factor of 108 and 116 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 116


2 116
2 58
29 29
1

Prime factors of 116 are 2,29. Prime factorization of 116 in exponential form is:

116 = 22×291

∴ So by taking common prime factors GCF of 108 and 116 is 4

Greatest Common Factor of 108 and 116 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 116

List of positive integer factors of 116 that divides 116 without a remainder.

1,2,4,29,58,116

Greatest Common Factor

We found the factors and prime factorization of 108 and 116. The biggest common factor number is the GCF number.
So the greatest common factor 108 and 116 is 4.

Also check out the Least Common Multiple of 108 and 116

Properties of GCF 108 and 116

(i) The GCF of 108 and 116 is associative

GCF of 108 and 116 = GCF of 116 and 108

Frequently Asked Questions on GCF of 108 and 116

1. What is the GCF of 108 and 116?

Answer: GCF of 108 and 116 is 4.

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 116?

Answer: Factors of 116 are 1, 2, 4, 29, 58, 116. There are 6 integers that are factors of 116. The greatest factor of 116 is 116.

4. How to Find the GCF of 108 and 116?

Answer:

Greatest Common Factor of 108 and 116 = 4

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 116

116 = 2 x 2 x 29

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

GCF = 2 x 2 = 4

Step 4: Therefore, the greatest common factor of 108 and 116 is 4