Solution: The GCF of 111 and 42 is 3
Methods
How to find the GCF of 111 and 42 using Prime Factorization
One way to find the GCF of 111 and 42 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 42?
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 42:
2
1
×
3
1
×
7
1
2^1 × 3^1 × 7^1
2 1 × 3 1 × 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 42 by multiplying all the matching prime factors to get a GCF of 111 and 42 as 9:
Thus, the GCF of 111 and 42 is: 9
How to Find the GCF of 111 and 42 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 111 and 42 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 42:
Factors of 111: 1, 3, 37, 111
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
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 42 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 8 and 74?
What is the GCF of 53 and 110?
What is the GCF of 105 and 123?
What is the GCF of 66 and 2?
What is the GCF of 135 and 19?