Solution: The GCF of 138 and 3 is 3
Methods
How to find the GCF of 138 and 3 using Prime Factorization
One way to find the GCF of 138 and 3 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 3?
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 3:
3
1
3^1
3 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 3 by multiplying all the matching prime factors to get a GCF of 138 and 3 as 9:
Thus, the GCF of 138 and 3 is: 9
How to Find the GCF of 138 and 3 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 138 and 3 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 3:
Factors of 138: 1, 2, 3, 6, 23, 46, 69, 138
Factors of 3: 1, 3
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 138 and 3 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 31 and 19?
What is the GCF of 36 and 93?
What is the GCF of 3 and 70?
What is the GCF of 14 and 91?
What is the GCF of 64 and 59?