Solution: The GCF of 123 and 39 is 3
Methods
How to find the GCF of 123 and 39 using Prime Factorization
One way to find the GCF of 123 and 39 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 123?
What are the Factors of 39?
Here is the prime factorization of 123:
3
1
×
4
1
1
3^1 × 41^1
3 1 × 4 1 1
And this is the prime factorization of 39:
3
1
×
1
3
1
3^1 × 13^1
3 1 × 1 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 123 and 39 by multiplying all the matching prime factors to get a GCF of 123 and 39 as 9:
Thus, the GCF of 123 and 39 is: 9
How to Find the GCF of 123 and 39 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 123 and 39 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, 123 and 39:
Factors of 123: 1, 3, 41, 123
Factors of 39: 1, 3, 13, 39
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 123 and 39 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 122 and 4?
What is the GCF of 40 and 72?
What is the GCF of 61 and 52?
What is the GCF of 124 and 82?
What is the GCF of 26 and 78?