Greatest Common Factor of 120 and 180

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 120, 180 i.e. 60 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 120 and 180 is 60.

GCF(120,180) = 60

GCF of 120 and 180

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

GCF of:
and

Greatest Common Factor of 120 and 180

GCF of 120 and 180 is 60

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

Prime Factorization of 180


2 180
2 90
3 45
3 15
5 5
1

Prime factors of 180 are 2,3,5. Prime factorization of 180 in exponential form is:

180 = 22×32×51

∴ So by taking common prime factors GCF of 120 and 180 is 60

Greatest Common Factor of 120 and 180 by matching factors method

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

Factors of 180

List of positive integer factors of 180 that divides 180 without a remainder.

1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180

Greatest Common Factor

We found the factors and prime factorization of 120 and 180. The biggest common factor number is the GCF number.
So the greatest common factor 120 and 180 is 60.

Also check out the Least Common Multiple of 120 and 180

Properties of GCF 120 and 180

(i) The GCF of 120 and 180 is associative

GCF of 120 and 180 = GCF of 180 and 120

Related Greatest Common Factor of 120

Related Greatest Common Factor of 180

Frequently Asked Questions on GCF of 120 and 180

1. What is the GCF of 120 and 180?

Answer: GCF of 120 and 180 is 60.

2. 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.

3. What are the Factors of 180?

Answer: Factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180. There are 18 integers that are factors of 180. The greatest factor of 180 is 180.

4. How to Find the GCF of 120 and 180?

Answer:

Greatest Common Factor of 120 and 180 = 60

Step 1: Find the prime factorization of 120

120 = 2 x 2 x 2 x 3 x 5

Step 2: Find the prime factorization of 180

180 = 2 x 2 x 3 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 2 x 3 x 5 = 60

Step 4: Therefore, the greatest common factor of 120 and 180 is 60