Solution: The GCF of 111 and 123 is 3
Methods
How to find the GCF of 111 and 123 using Prime Factorization
One way to find the GCF of 111 and 123 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 111?
What are the Factors of 123?
Here is the prime factorization of 111:
3
1
×
3
7
1
3^1 × 37^1
3 1 × 3 7 1
And this is the prime factorization of 123:
3
1
×
4
1
1
3^1 × 41^1
3 1 × 4 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 111 and 123 by multiplying all the matching prime factors to get a GCF of 111 and 123 as 9:
Thus, the GCF of 111 and 123 is: 9
How to Find the GCF of 111 and 123 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 111 and 123 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, 111 and 123:
Factors of 111: 1, 3, 37, 111
Factors of 123: 1, 3, 41, 123
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 111 and 123 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 91 and 98?
What is the GCF of 17 and 77?
What is the GCF of 64 and 124?
What is the GCF of 15 and 138?
What is the GCF of 70 and 135?