Solution: The GCF of 14 and 112 is 14
Methods
How to find the GCF of 14 and 112 using Prime Factorization
One way to find the GCF of 14 and 112 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 112?
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 112:
2
4
×
7
1
2^4 × 7^1
2 4 × 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 112 by multiplying all the matching prime factors to get a GCF of 14 and 112 as 196:
Thus, the GCF of 14 and 112 is: 196
How to Find the GCF of 14 and 112 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 14 and 112 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 112:
Factors of 14: 1, 2, 7, 14
Factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112
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 112 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 67 and 125?
What is the GCF of 146 and 133?
What is the GCF of 130 and 7?
What is the GCF of 113 and 65?
What is the GCF of 82 and 28?