Solution: The GCF of 74 and 111 is 37
Methods
How to find the GCF of 74 and 111 using Prime Factorization
One way to find the GCF of 74 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 74?
What are the Factors of 111?
Here is the prime factorization of 74:
2
1
×
3
7
1
2^1 × 37^1
2 1 × 3 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 74 and 111 by multiplying all the matching prime factors to get a GCF of 74 and 111 as 1369:
Thus, the GCF of 74 and 111 is: 1369
How to Find the GCF of 74 and 111 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 74 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, 74 and 111:
Factors of 74: 1, 2, 37, 74
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, 37. Since 37 is the largest of these common factors, the GCF of 74 and 111 would be 37.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 54 and 63?
What is the GCF of 143 and 131?
What is the GCF of 7 and 15?
What is the GCF of 92 and 58?
What is the GCF of 40 and 42?