Solution: The GCF of 120 and 126 is 6
Methods
How to find the GCF of 120 and 126 using Prime Factorization
One way to find the GCF of 120 and 126 is to compare the prime factorization of each number. To find the prime factorization, you can follow the instructions for each number here:
What are the Factors of 120?
What are the Factors of 126?
Here is the prime factorization of 120:
2
3
×
3
1
×
5
1
2^3 × 3^1 × 5^1
2 3 × 3 1 × 5 1
And this is the prime factorization of 126:
2
1
×
3
2
×
7
1
2^1 × 3^2 × 7^1
2 1 × 3 2 × 7 1
When you compare the prime factorization of these two numbers, you can see that there are matching prime factors. You can now find the Greatest Common Factor of 120 and 126 by multiplying all the matching prime factors to get a GCF of 120 and 126 as 36:
Thus, the GCF of 120 and 126 is: 36
How to Find the GCF of 120 and 126 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 120 and 126 is to find and list all the factors of each number. Again, you can see how this is done by looking at the “Factors of” articles that are linked to above.
Let’s take a look at the factors for each of these numbers, 120 and 126:
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 3, 6. Since 6 is the largest of these common factors, the GCF of 120 and 126 would be 6.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 73 and 81?
What is the GCF of 109 and 51?
What is the GCF of 24 and 56?
What is the GCF of 22 and 47?
What is the GCF of 17 and 108?