Solution: The GCF of 14 and 56 is 14
Methods
How to find the GCF of 14 and 56 using Prime Factorization
One way to find the GCF of 14 and 56 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 14?
What are the Factors of 56?
Here is the prime factorization of 14:
2
1
×
7
1
2^1 × 7^1
2 1 × 7 1
And this is the prime factorization of 56:
2
3
×
7
1
2^3 × 7^1
2 3 × 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 14 and 56 by multiplying all the matching prime factors to get a GCF of 14 and 56 as 196:
Thus, the GCF of 14 and 56 is: 196
How to Find the GCF of 14 and 56 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 14 and 56 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, 14 and 56:
Factors of 14: 1, 2, 7, 14
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 7, 14. Since 14 is the largest of these common factors, the GCF of 14 and 56 would be 14.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 118 and 41?
What is the GCF of 34 and 80?
What is the GCF of 101 and 23?
What is the GCF of 3 and 7?
What is the GCF of 84 and 132?