Greatest Common Factor of 120 and 126

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

Greatest common factor (GCF) of 120 and 126 is 6.

GCF(120,126) = 6

GCF of 120 and 126

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

GCF of:
and

Greatest Common Factor of 120 and 126

GCF of 120 and 126 is 6

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 126


2 126
3 63
3 21
7 7
1

Prime factors of 126 are 2,3,7. Prime factorization of 126 in exponential form is:

126 = 21×32×71

∴ So by taking common prime factors GCF of 120 and 126 is 6

Greatest Common Factor of 120 and 126 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 126

List of positive integer factors of 126 that divides 126 without a remainder.

1,2,3,6,7,9,14,18,21,42,63,126

Greatest Common Factor

We found the factors and prime factorization of 120 and 126. The biggest common factor number is the GCF number.
So the greatest common factor 120 and 126 is 6.

Also check out the Least Common Multiple of 120 and 126

Properties of GCF 120 and 126

(i) The GCF of 120 and 126 is associative

GCF of 120 and 126 = GCF of 126 and 120

Related Greatest Common Factor of 120

Related Greatest Common Factor of 126

Frequently Asked Questions on GCF of 120 and 126

1. What is the GCF of 120 and 126?

Answer: GCF of 120 and 126 is 6.

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 126?

Answer: Factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126. There are 12 integers that are factors of 126. The greatest factor of 126 is 126.

4. How to Find the GCF of 120 and 126?

Answer:

Greatest Common Factor of 120 and 126 = 6

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 126

126 = 2 x 3 x 3 x 7

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 120 and 126 is 6