Greatest Common Factor of 96 and 114

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 96, 114 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 96 and 114 is 6.

GCF(96,114) = 6

GCF of 96 and 114

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

GCF of:
and

Greatest Common Factor of 96 and 114

GCF of 96 and 114 is 6

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 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 96 and 114 is 6

Greatest Common Factor of 96 and 114 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 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 96 and 114. The biggest common factor number is the GCF number.
So the greatest common factor 96 and 114 is 6.

Also check out the Least Common Multiple of 96 and 114

Properties of GCF 96 and 114

(i) The GCF of 96 and 114 is associative

GCF of 96 and 114 = GCF of 114 and 96

Related Greatest Common Factor of 96

Related Greatest Common Factor of 114

Frequently Asked Questions on GCF of 96 and 114

1. What is the GCF of 96 and 114?

Answer: GCF of 96 and 114 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 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 96 and 114?

Answer:

Greatest Common Factor of 96 and 114 = 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 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 96 and 114 is 6