Solution: The GCF of 84 and 51 is 3
Methods
How to find the GCF of 84 and 51 using Prime Factorization
One way to find the GCF of 84 and 51 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 84?
What are the Factors of 51?
Here is the prime factorization of 84:
2
2
×
3
1
×
7
1
2^2 × 3^1 × 7^1
2 2 × 3 1 × 7 1
And this is the prime factorization of 51:
3
1
×
1
7
1
3^1 × 17^1
3 1 × 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 84 and 51 by multiplying all the matching prime factors to get a GCF of 84 and 51 as 9:
Thus, the GCF of 84 and 51 is: 9
How to Find the GCF of 84 and 51 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 84 and 51 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, 84 and 51:
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Factors of 51: 1, 3, 17, 51
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 84 and 51 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 120 and 77?
What is the GCF of 112 and 92?
What is the GCF of 105 and 1?
What is the GCF of 28 and 65?
What is the GCF of 53 and 20?