Solution: The GCF of 144 and 92 is 4
Methods
How to find the GCF of 144 and 92 using Prime Factorization
One way to find the GCF of 144 and 92 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 92?
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 92:
2
2
×
2
3
1
2^2 × 23^1
2 2 × 2 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 144 and 92 by multiplying all the matching prime factors to get a GCF of 144 and 92 as 4:
Thus, the GCF of 144 and 92 is: 4
How to Find the GCF of 144 and 92 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 144 and 92 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 92:
Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Factors of 92: 1, 2, 4, 23, 46, 92
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 4. Since 4 is the largest of these common factors, the GCF of 144 and 92 would be 4.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 24 and 56?
What is the GCF of 126 and 146?
What is the GCF of 118 and 95?
What is the GCF of 2 and 78?
What is the GCF of 119 and 30?