Solution: The GCF of 144 and 126 is 18
Methods
How to find the GCF of 144 and 126 using Prime Factorization
One way to find the GCF of 144 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 144?
What are the Factors of 126?
Here is the prime factorization of 144:
2
4
×
3
2
2^4 × 3^2
2 4 × 3 2
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 144 and 126 by multiplying all the matching prime factors to get a GCF of 144 and 126 as 36:
Thus, the GCF of 144 and 126 is: 36
How to Find the GCF of 144 and 126 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 144 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, 144 and 126:
Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
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, 9, 18. Since 18 is the largest of these common factors, the GCF of 144 and 126 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 127 and 125?
What is the GCF of 110 and 104?
What is the GCF of 17 and 136?
What is the GCF of 130 and 66?
What is the GCF of 71 and 12?