Solution: The GCF of 54 and 150 is 6
Methods
How to find the GCF of 54 and 150 using Prime Factorization
One way to find the GCF of 54 and 150 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 54?
What are the Factors of 150?
Here is the prime factorization of 54:
2
1
×
3
3
2^1 × 3^3
2 1 × 3 3
And this is the prime factorization of 150:
2
1
×
3
1
×
5
2
2^1 × 3^1 × 5^2
2 1 × 3 1 × 5 2
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 54 and 150 by multiplying all the matching prime factors to get a GCF of 54 and 150 as 36:
Thus, the GCF of 54 and 150 is: 36
How to Find the GCF of 54 and 150 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 54 and 150 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, 54 and 150:
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
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 54 and 150 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 105 and 28?
What is the GCF of 24 and 42?
What is the GCF of 26 and 103?
What is the GCF of 118 and 37?
What is the GCF of 113 and 52?