Solution: The GCF of 106 and 14 is 2
Methods
How to find the GCF of 106 and 14 using Prime Factorization
One way to find the GCF of 106 and 14 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 106?
What are the Factors of 14?
Here is the prime factorization of 106:
2
1
×
5
3
1
2^1 × 53^1
2 1 × 5 3 1
And this is the prime factorization of 14:
2
1
×
7
1
2^1 × 7^1
2 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 106 and 14 by multiplying all the matching prime factors to get a GCF of 106 and 14 as 4:
Thus, the GCF of 106 and 14 is: 4
How to Find the GCF of 106 and 14 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 106 and 14 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, 106 and 14:
Factors of 106: 1, 2, 53, 106
Factors of 14: 1, 2, 7, 14
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2. Since 2 is the largest of these common factors, the GCF of 106 and 14 would be 2.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 63 and 61?
What is the GCF of 124 and 86?
What is the GCF of 34 and 24?
What is the GCF of 69 and 132?
What is the GCF of 100 and 125?