Greatest Common Factor of 120 and 123

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, 123 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 120 and 123 is 3.

GCF(120,123) = 3

GCF of 120 and 123

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

GCF of:
and

Greatest Common Factor of 120 and 123

GCF of 120 and 123 is 3

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 123


3 123
41 41
1

Prime factors of 123 are 3,41. Prime factorization of 123 in exponential form is:

123 = 31×411

∴ So by taking common prime factors GCF of 120 and 123 is 3

Greatest Common Factor of 120 and 123 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 123

List of positive integer factors of 123 that divides 123 without a remainder.

1,3,41,123

Greatest Common Factor

We found the factors and prime factorization of 120 and 123. The biggest common factor number is the GCF number.
So the greatest common factor 120 and 123 is 3.

Also check out the Least Common Multiple of 120 and 123

Properties of GCF 120 and 123

(i) The GCF of 120 and 123 is associative

GCF of 120 and 123 = GCF of 123 and 120

Related Greatest Common Factor of 120

Related Greatest Common Factor of 123

Frequently Asked Questions on GCF of 120 and 123

1. What is the GCF of 120 and 123?

Answer: GCF of 120 and 123 is 3.

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 123?

Answer: Factors of 123 are 1, 3, 41, 123. There are 4 integers that are factors of 123. The greatest factor of 123 is 123.

4. How to Find the GCF of 120 and 123?

Answer:

Greatest Common Factor of 120 and 123 = 3

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 123

123 = 3 x 41

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

GCF = 3

Step 4: Therefore, the greatest common factor of 120 and 123 is 3