Solution: The GCF of 84 and 77 is 7
Methods
How to find the GCF of 84 and 77 using Prime Factorization
One way to find the GCF of 84 and 77 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 77?
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 77:
7
1
×
1
1
1
7^1 × 11^1
7 1 × 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 84 and 77 by multiplying all the matching prime factors to get a GCF of 84 and 77 as 49:
Thus, the GCF of 84 and 77 is: 49
How to Find the GCF of 84 and 77 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 84 and 77 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 77:
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Factors of 77: 1, 7, 11, 77
When you compare the two lists of factors, you can see that the common factor(s) are 1, 7. Since 7 is the largest of these common factors, the GCF of 84 and 77 would be 7.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 51 and 148?
What is the GCF of 77 and 78?
What is the GCF of 50 and 55?
What is the GCF of 123 and 43?
What is the GCF of 27 and 99?