Solution: The GCF of 28 and 84 is 28
Methods
How to find the GCF of 28 and 84 using Prime Factorization
One way to find the GCF of 28 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 28?
What are the Factors of 84?
Here is the prime factorization of 28:
2
2
×
7
1
2^2 × 7^1
2 2 × 7 1
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 28 and 84 by multiplying all the matching prime factors to get a GCF of 28 and 84 as 196:
Thus, the GCF of 28 and 84 is: 196
How to Find the GCF of 28 and 84 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 28 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, 28 and 84:
Factors of 28: 1, 2, 4, 7, 14, 28
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, 2, 4, 7, 14, 28. Since 28 is the largest of these common factors, the GCF of 28 and 84 would be 28.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 56 and 68?
What is the GCF of 107 and 136?
What is the GCF of 118 and 27?
What is the GCF of 40 and 3?
What is the GCF of 82 and 55?