Solution: The GCF of 126 and 6 is 6
Methods
How to find the GCF of 126 and 6 using Prime Factorization
One way to find the GCF of 126 and 6 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 126?
What are the Factors of 6?
Here is the prime factorization of 126:
2
1
×
3
2
×
7
1
2^1 × 3^2 × 7^1
2 1 × 3 2 × 7 1
And this is the prime factorization of 6:
2
1
×
3
1
2^1 × 3^1
2 1 × 3 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 126 and 6 by multiplying all the matching prime factors to get a GCF of 126 and 6 as 36:
Thus, the GCF of 126 and 6 is: 36
How to Find the GCF of 126 and 6 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 126 and 6 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, 126 and 6:
Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
Factors of 6: 1, 2, 3, 6
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 126 and 6 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 2 and 6?
What is the GCF of 111 and 79?
What is the GCF of 139 and 23?
What is the GCF of 13 and 112?
What is the GCF of 109 and 150?