Solution: The GCF of 111 and 57 is 3
Methods
How to find the GCF of 111 and 57 using Prime Factorization
One way to find the GCF of 111 and 57 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 57?
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 57:
3
1
×
1
9
1
3^1 × 19^1
3 1 × 1 9 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 57 by multiplying all the matching prime factors to get a GCF of 111 and 57 as 9:
Thus, the GCF of 111 and 57 is: 9
How to Find the GCF of 111 and 57 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 111 and 57 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 57:
Factors of 111: 1, 3, 37, 111
Factors of 57: 1, 3, 19, 57
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 57 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 54 and 73?
What is the GCF of 134 and 147?
What is the GCF of 19 and 25?
What is the GCF of 78 and 36?
What is the GCF of 49 and 125?