Solution: The GCF of 105 and 133 is 7
Methods
How to find the GCF of 105 and 133 using Prime Factorization
One way to find the GCF of 105 and 133 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 105?
What are the Factors of 133?
Here is the prime factorization of 105:
3
1
×
5
1
×
7
1
3^1 × 5^1 × 7^1
3 1 × 5 1 × 7 1
And this is the prime factorization of 133:
7
1
×
1
9
1
7^1 × 19^1
7 1 × 1 9 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 105 and 133 by multiplying all the matching prime factors to get a GCF of 105 and 133 as 49:
Thus, the GCF of 105 and 133 is: 49
How to Find the GCF of 105 and 133 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 105 and 133 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, 105 and 133:
Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105
Factors of 133: 1, 7, 19, 133
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 105 and 133 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 5 and 124?
What is the GCF of 107 and 83?
What is the GCF of 56 and 131?
What is the GCF of 143 and 133?
What is the GCF of 66 and 68?