# Greatest Common Factor of 108 and 112

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 108, 112 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 108 and 112 is 4.

GCF(108,112) = 4

## GCF of 108 and 112

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

GCF of:
and

### Greatest Common Factor of 108 and 112 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 112

 2 112 2 56 2 28 2 14 7 7 1

Prime factors of 112 are 2,7. Prime factorization of 112 in exponential form is:

112 = 24×71

∴ So by taking common prime factors GCF of 108 and 112 is 4

### Greatest Common Factor of 108 and 112 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 112

List of positive integer factors of 112 that divides 112 without a remainder.

1,2,4,7,8,14,16,28,56,112

Greatest Common Factor

We found the factors and prime factorization of 108 and 112. The biggest common factor number is the GCF number.
So the greatest common factor 108 and 112 is 4.

Also check out the Least Common Multiple of 108 and 112

### Properties of GCF 108 and 112

(i) The GCF of 108 and 112 is associative

GCF of 108 and 112 = GCF of 112 and 108

### Frequently Asked Questions on GCF of 108 and 112

1. What is the GCF of 108 and 112?

Answer: GCF of 108 and 112 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 112?

Answer: Factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112. There are 10 integers that are factors of 112. The greatest factor of 112 is 112.

4. How to Find the GCF of 108 and 112?

Greatest Common Factor of 108 and 112 = 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 112

112 = 2 x 2 x 2 x 2 x 7

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 112 is 4