Solution: The GCF of 49 and 91 is 7
Methods
How to find the GCF of 49 and 91 using Prime Factorization
One way to find the GCF of 49 and 91 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 49?
What are the Factors of 91?
Here is the prime factorization of 49:
7
2
7^2
7 2
And this is the prime factorization of 91:
7
1
×
1
3
1
7^1 × 13^1
7 1 × 1 3 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 49 and 91 by multiplying all the matching prime factors to get a GCF of 49 and 91 as 49:
Thus, the GCF of 49 and 91 is: 49
How to Find the GCF of 49 and 91 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 49 and 91 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, 49 and 91:
Factors of 49: 1, 7, 49
Factors of 91: 1, 7, 13, 91
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 49 and 91 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 36 and 70?
What is the GCF of 78 and 26?
What is the GCF of 48 and 47?
What is the GCF of 140 and 94?
What is the GCF of 104 and 60?