Solution: The GCF of 30 and 99 is 3
Methods
How to find the GCF of 30 and 99 using Prime Factorization
One way to find the GCF of 30 and 99 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 30?
What are the Factors of 99?
Here is the prime factorization of 30:
2
1
×
3
1
×
5
1
2^1 × 3^1 × 5^1
2 1 × 3 1 × 5 1
And this is the prime factorization of 99:
3
2
×
1
1
1
3^2 × 11^1
3 2 × 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 30 and 99 by multiplying all the matching prime factors to get a GCF of 30 and 99 as 9:
Thus, the GCF of 30 and 99 is: 9
How to Find the GCF of 30 and 99 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 30 and 99 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, 30 and 99:
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 99: 1, 3, 9, 11, 33, 99
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 30 and 99 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 141 and 17?
What is the GCF of 118 and 74?
What is the GCF of 4 and 148?
What is the GCF of 130 and 32?
What is the GCF of 123 and 149?