# Greatest Common Factor of 84 and 96

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 84, 96 i.e. 12 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 84 and 96 is 12.

GCF(84,96) = 12

## GCF of 84 and 96

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

GCF of:
and ### GCF of 84 and 96 is 12

Prime Factorization of 84

 2 84 2 42 3 21 7 7 1

Prime factors of 84 are 2,3,7. Prime factorization of 84 in exponential form is:

84 = 22×31×71

Prime Factorization of 96

 2 96 2 48 2 24 2 12 2 6 3 3 1

Prime factors of 96 are 2,3. Prime factorization of 96 in exponential form is:

96 = 25×31

∴ So by taking common prime factors GCF of 84 and 96 is 12

### Greatest Common Factor of 84 and 96 by matching factors method

Factors of 84

List of positive integer factors of 84 that divides 84 without a remainder.

1,2,3,4,6,7,12,14,21,28,42,84

Factors of 96

List of positive integer factors of 96 that divides 96 without a remainder.

1,2,3,4,6,8,12,16,24,32,48,96

Greatest Common Factor

We found the factors and prime factorization of 84 and 96. The biggest common factor number is the GCF number.
So the greatest common factor 84 and 96 is 12.

Also check out the Least Common Multiple of 84 and 96

### Properties of GCF 84 and 96

(i) The GCF of 84 and 96 is associative

GCF of 84 and 96 = GCF of 96 and 84

### Frequently Asked Questions on GCF of 84 and 96

1. What is the GCF of 84 and 96?

Answer: GCF of 84 and 96 is 12.

2. What are the Factors of 84?

Answer: Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. There are 12 integers that are factors of 84. The greatest factor of 84 is 84.

3. What are the Factors of 96?

Answer: Factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96. There are 12 integers that are factors of 96. The greatest factor of 96 is 96.

4. How to Find the GCF of 84 and 96?

Greatest Common Factor of 84 and 96 = 12

Step 1: Find the prime factorization of 84

84 = 2 x 2 x 3 x 7

Step 2: Find the prime factorization of 96

96 = 2 x 2 x 2 x 2 x 2 x 3

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

GCF = 2 x 2 x 3 = 12

Step 4: Therefore, the greatest common factor of 84 and 96 is 12