Solution: The GCF of 126 and 72 is 18
Methods
How to find the GCF of 126 and 72 using Prime Factorization
One way to find the GCF of 126 and 72 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 72?
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 72:
2
3
×
3
2
2^3 × 3^2
2 3 × 3 2
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 72 by multiplying all the matching prime factors to get a GCF of 126 and 72 as 36:
Thus, the GCF of 126 and 72 is: 36
How to Find the GCF of 126 and 72 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 126 and 72 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 72:
Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 3, 6, 9, 18. Since 18 is the largest of these common factors, the GCF of 126 and 72 would be 18.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 17 and 80?
What is the GCF of 127 and 83?
What is the GCF of 100 and 102?
What is the GCF of 51 and 91?
What is the GCF of 20 and 67?