Solution: The GCF of 12 and 126 is 6
Methods
How to find the GCF of 12 and 126 using Prime Factorization
One way to find the GCF of 12 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 12?
What are the Factors of 126?
Here is the prime factorization of 12:
2
2
×
3
1
2^2 × 3^1
2 2 × 3 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 12 and 126 by multiplying all the matching prime factors to get a GCF of 12 and 126 as 36:
Thus, the GCF of 12 and 126 is: 36
How to Find the GCF of 12 and 126 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 12 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, 12 and 126:
Factors of 12: 1, 2, 3, 4, 6, 12
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 12 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 90 and 66?
What is the GCF of 27 and 118?
What is the GCF of 123 and 138?
What is the GCF of 2 and 129?
What is the GCF of 56 and 100?