Solution: The GCF of 138 and 38 is 2
Methods
How to find the GCF of 138 and 38 using Prime Factorization
One way to find the GCF of 138 and 38 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 138?
What are the Factors of 38?
Here is the prime factorization of 138:
2
1
×
3
1
×
2
3
1
2^1 × 3^1 × 23^1
2 1 × 3 1 × 2 3 1
And this is the prime factorization of 38:
2
1
×
1
9
1
2^1 × 19^1
2 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 138 and 38 by multiplying all the matching prime factors to get a GCF of 138 and 38 as 4:
Thus, the GCF of 138 and 38 is: 4
How to Find the GCF of 138 and 38 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 138 and 38 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, 138 and 38:
Factors of 138: 1, 2, 3, 6, 23, 46, 69, 138
Factors of 38: 1, 2, 19, 38
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2. Since 2 is the largest of these common factors, the GCF of 138 and 38 would be 2.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 61 and 88?
What is the GCF of 71 and 4?
What is the GCF of 56 and 81?
What is the GCF of 108 and 143?
What is the GCF of 127 and 80?