Greatest Common Factor of 114 and 120

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 114, 120 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 114 and 120 is 6.

GCF(114,120) = 6

GCF of 114 and 120

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

GCF of:
and

Greatest Common Factor of 114 and 120

GCF of 114 and 120 is 6

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

Prime Factorization of 120


2 120
2 60
2 30
3 15
5 5
1

Prime factors of 120 are 2,3,5. Prime factorization of 120 in exponential form is:

120 = 23×31×51

∴ So by taking common prime factors GCF of 114 and 120 is 6

Greatest Common Factor of 114 and 120 by matching factors method

Factors of 114

List of positive integer factors of 114 that divides 114 without a remainder.

1,2,3,6,19,38,57,114

Factors of 120

List of positive integer factors of 120 that divides 120 without a remainder.

1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120

Greatest Common Factor

We found the factors and prime factorization of 114 and 120. The biggest common factor number is the GCF number.
So the greatest common factor 114 and 120 is 6.

Also check out the Least Common Multiple of 114 and 120

Properties of GCF 114 and 120

(i) The GCF of 114 and 120 is associative

GCF of 114 and 120 = GCF of 120 and 114

Related Greatest Common Factor of 114

Related Greatest Common Factor of 120

Frequently Asked Questions on GCF of 114 and 120

1. What is the GCF of 114 and 120?

Answer: GCF of 114 and 120 is 6.

2. 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.

3. What are the Factors of 120?

Answer: Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. There are 16 integers that are factors of 120. The greatest factor of 120 is 120.

4. How to Find the GCF of 114 and 120?

Answer:

Greatest Common Factor of 114 and 120 = 6

Step 1: Find the prime factorization of 114

114 = 2 x 3 x 19

Step 2: Find the prime factorization of 120

120 = 2 x 2 x 2 x 3 x 5

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 114 and 120 is 6