Solution: The GCF of 27 and 84 is 3
Methods
How to find the GCF of 27 and 84 using Prime Factorization
One way to find the GCF of 27 and 84 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 27?
What are the Factors of 84?
Here is the prime factorization of 27:
3
3
3^3
3 3
And this is the prime factorization of 84:
2
2
×
3
1
×
7
1
2^2 × 3^1 × 7^1
2 2 × 3 1 × 7 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 27 and 84 by multiplying all the matching prime factors to get a GCF of 27 and 84 as 9:
Thus, the GCF of 27 and 84 is: 9
How to Find the GCF of 27 and 84 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 27 and 84 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, 27 and 84:
Factors of 27: 1, 3, 9, 27
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
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 27 and 84 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 122 and 95?
What is the GCF of 51 and 63?
What is the GCF of 48 and 91?
What is the GCF of 108 and 100?
What is the GCF of 25 and 96?