Solution: The GCF of 100 and 22 is 2
Methods
How to find the GCF of 100 and 22 using Prime Factorization
One way to find the GCF of 100 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 100?
What are the Factors of 22?
Here is the prime factorization of 100:
2
2
×
5
2
2^2 × 5^2
2 2 × 5 2
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 100 and 22 by multiplying all the matching prime factors to get a GCF of 100 and 22 as 4:
Thus, the GCF of 100 and 22 is: 4
How to Find the GCF of 100 and 22 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 100 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, 100 and 22:
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
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 100 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 42 and 96?
What is the GCF of 122 and 80?
What is the GCF of 19 and 89?
What is the GCF of 60 and 136?
What is the GCF of 104 and 49?