Solution: The GCF of 138 and 106 is 2
Methods
How to find the GCF of 138 and 106 using Prime Factorization
One way to find the GCF of 138 and 106 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 106?
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 106:
2
1
×
5
3
1
2^1 × 53^1
2 1 × 5 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 106 by multiplying all the matching prime factors to get a GCF of 138 and 106 as 4:
Thus, the GCF of 138 and 106 is: 4
How to Find the GCF of 138 and 106 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 138 and 106 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 106:
Factors of 138: 1, 2, 3, 6, 23, 46, 69, 138
Factors of 106: 1, 2, 53, 106
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 106 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 150?
What is the GCF of 100 and 78?
What is the GCF of 48 and 111?
What is the GCF of 43 and 72?
What is the GCF of 130 and 80?