Solution: The GCF of 111 and 63 is 3
Methods
How to find the GCF of 111 and 63 using Prime Factorization
One way to find the GCF of 111 and 63 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 63?
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 63:
3
2
×
7
1
3^2 × 7^1
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 111 and 63 by multiplying all the matching prime factors to get a GCF of 111 and 63 as 9:
Thus, the GCF of 111 and 63 is: 9
How to Find the GCF of 111 and 63 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 111 and 63 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 63:
Factors of 111: 1, 3, 37, 111
Factors of 63: 1, 3, 7, 9, 21, 63
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 63 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 116 and 120?
What is the GCF of 77 and 117?
What is the GCF of 129 and 115?
What is the GCF of 22 and 3?
What is the GCF of 12 and 30?