# Greatest Common Factor of 96 and 102

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 96, 102 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 96 and 102 is 6.

GCF(96,102) = 6

## GCF of 96 and 102

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

GCF of:
and

### Greatest Common Factor of 96 and 102 by Prime factorization method

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

Prime Factorization of 102

 2 102 3 51 17 17 1

Prime factors of 102 are 2,3,17. Prime factorization of 102 in exponential form is:

102 = 21×31×171

∴ So by taking common prime factors GCF of 96 and 102 is 6

### Greatest Common Factor of 96 and 102 by matching factors method

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

Factors of 102

List of positive integer factors of 102 that divides 102 without a remainder.

1,2,3,6,17,34,51,102

Greatest Common Factor

We found the factors and prime factorization of 96 and 102. The biggest common factor number is the GCF number.
So the greatest common factor 96 and 102 is 6.

Also check out the Least Common Multiple of 96 and 102

### Properties of GCF 96 and 102

(i) The GCF of 96 and 102 is associative

GCF of 96 and 102 = GCF of 102 and 96

### Frequently Asked Questions on GCF of 96 and 102

1. What is the GCF of 96 and 102?

Answer: GCF of 96 and 102 is 6.

2. 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.

3. What are the Factors of 102?

Answer: Factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102. There are 8 integers that are factors of 102. The greatest factor of 102 is 102.

4. How to Find the GCF of 96 and 102?

Answer:

Greatest Common Factor of 96 and 102 = 6

Step 1: Find the prime factorization of 96

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

Step 2: Find the prime factorization of 102

102 = 2 x 3 x 17

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 96 and 102 is 6