Solution: The GCF of 144 and 93 is 3
Methods
How to find the GCF of 144 and 93 using Prime Factorization
One way to find the GCF of 144 and 93 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 93?
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 93:
3
1
×
3
1
1
3^1 × 31^1
3 1 × 3 1 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 93 by multiplying all the matching prime factors to get a GCF of 144 and 93 as 9:
Thus, the GCF of 144 and 93 is: 9
How to Find the GCF of 144 and 93 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 144 and 93 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 93:
Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Factors of 93: 1, 3, 31, 93
When you compare the two lists of factors, you can see that the common factor(s) are 1, 3. Since 3 is the largest of these common factors, the GCF of 144 and 93 would be 3.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 138 and 30?
What is the GCF of 48 and 37?
What is the GCF of 49 and 77?
What is the GCF of 95 and 100?
What is the GCF of 64 and 65?