Solution: The GCF of 42 and 138 is 6
Methods
How to find the GCF of 42 and 138 using Prime Factorization
One way to find the GCF of 42 and 138 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 42?
What are the Factors of 138?
Here is the prime factorization of 42:
2
1
×
3
1
×
7
1
2^1 × 3^1 × 7^1
2 1 × 3 1 × 7 1
And this 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
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 42 and 138 by multiplying all the matching prime factors to get a GCF of 42 and 138 as 36:
Thus, the GCF of 42 and 138 is: 36
How to Find the GCF of 42 and 138 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 42 and 138 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, 42 and 138:
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
Factors of 138: 1, 2, 3, 6, 23, 46, 69, 138
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 3, 6. Since 6 is the largest of these common factors, the GCF of 42 and 138 would be 6.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 48 and 93?
What is the GCF of 86 and 57?
What is the GCF of 67 and 52?
What is the GCF of 7 and 116?
What is the GCF of 117 and 100?