Solution: The GCF of 38 and 22 is 2
Methods
How to find the GCF of 38 and 22 using Prime Factorization
One way to find the GCF of 38 and 22 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 38?
What are the Factors of 22?
Here is the prime factorization of 38:
2
1
×
1
9
1
2^1 × 19^1
2 1 × 1 9 1
And this is the prime factorization of 22:
2
1
×
1
1
1
2^1 × 11^1
2 1 × 1 1 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 38 and 22 by multiplying all the matching prime factors to get a GCF of 38 and 22 as 4:
Thus, the GCF of 38 and 22 is: 4
How to Find the GCF of 38 and 22 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 38 and 22 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, 38 and 22:
Factors of 38: 1, 2, 19, 38
Factors of 22: 1, 2, 11, 22
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 38 and 22 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 63 and 103?
What is the GCF of 59 and 147?
What is the GCF of 116 and 76?
What is the GCF of 114 and 36?
What is the GCF of 39 and 10?