Solution: The GCF of 126 and 28 is 14
Methods
How to find the GCF of 126 and 28 using Prime Factorization
One way to find the GCF of 126 and 28 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 28?
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 28:
2
2
×
7
1
2^2 × 7^1
2 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 126 and 28 by multiplying all the matching prime factors to get a GCF of 126 and 28 as 196:
Thus, the GCF of 126 and 28 is: 196
How to Find the GCF of 126 and 28 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 126 and 28 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 28:
Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
Factors of 28: 1, 2, 4, 7, 14, 28
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 7, 14. Since 14 is the largest of these common factors, the GCF of 126 and 28 would be 14.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 32 and 148?
What is the GCF of 93 and 78?
What is the GCF of 86 and 137?
What is the GCF of 73 and 116?
What is the GCF of 85 and 121?