Solution: The GCF of 21 and 111 is 3
Methods
How to find the GCF of 21 and 111 using Prime Factorization
One way to find the GCF of 21 and 111 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 21?
What are the Factors of 111?
Here is the prime factorization of 21:
3
1
×
7
1
3^1 × 7^1
3 1 × 7 1
And this is the prime factorization of 111:
3
1
×
3
7
1
3^1 × 37^1
3 1 × 3 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 21 and 111 by multiplying all the matching prime factors to get a GCF of 21 and 111 as 9:
Thus, the GCF of 21 and 111 is: 9
How to Find the GCF of 21 and 111 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 21 and 111 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, 21 and 111:
Factors of 21: 1, 3, 7, 21
Factors of 111: 1, 3, 37, 111
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 21 and 111 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 16 and 108?
What is the GCF of 31 and 139?
What is the GCF of 141 and 116?
What is the GCF of 60 and 122?
What is the GCF of 145 and 6?