Solution: The GCF of 37 and 148 is 37
Methods
How to find the GCF of 37 and 148 using Prime Factorization
One way to find the GCF of 37 and 148 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 37?
What are the Factors of 148?
Here is the prime factorization of 37:
3
7
1
37^1
3 7 1
And this is the prime factorization of 148:
2
2
×
3
7
1
2^2 × 37^1
2 2 × 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 37 and 148 by multiplying all the matching prime factors to get a GCF of 37 and 148 as 1369:
Thus, the GCF of 37 and 148 is: 1369
How to Find the GCF of 37 and 148 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 37 and 148 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, 37 and 148:
Factors of 37: 1, 37
Factors of 148: 1, 2, 4, 37, 74, 148
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 37 and 148 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 112 and 123?
What is the GCF of 45 and 142?
What is the GCF of 109 and 101?
What is the GCF of 67 and 74?
What is the GCF of 124 and 79?