Solution: The GCF of 77 and 70 is 7
Methods
How to find the GCF of 77 and 70 using Prime Factorization
One way to find the GCF of 77 and 70 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 77?
What are the Factors of 70?
Here is the prime factorization of 77:
7
1
×
1
1
1
7^1 × 11^1
7 1 × 1 1 1
And this is the prime factorization of 70:
2
1
×
5
1
×
7
1
2^1 × 5^1 × 7^1
2 1 × 5 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 77 and 70 by multiplying all the matching prime factors to get a GCF of 77 and 70 as 49:
Thus, the GCF of 77 and 70 is: 49
How to Find the GCF of 77 and 70 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 77 and 70 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, 77 and 70:
Factors of 77: 1, 7, 11, 77
Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70
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 77 and 70 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 31 and 26?
What is the GCF of 132 and 48?
What is the GCF of 14 and 150?
What is the GCF of 55 and 51?
What is the GCF of 35 and 141?