Solution: The GCF of 105 and 101 is 1
Methods
How to find the GCF of 105 and 101 using Prime Factorization
One way to find the GCF of 105 and 101 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 101?
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 101:
10
1
1
101^1
10 1 1
When you compare the prime factorization of these two numbers, you can see that there are no matching prime factors. When this is the case, it means that there are no common factors between these two numbers. As a result, the GCF of 105 and 101 is 1.
Thus, the GCF of 105 and 101 is: 1
How to Find the GCF of 105 and 101 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 105 and 101 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 101:
Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105
Factors of 101: 1, 101
When you compare the two lists of factors, you can see that the only common factor is 1. So, in this case, the GCF of 105 and 101 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 30 and 10?
What is the GCF of 109 and 82?
What is the GCF of 99 and 47?
What is the GCF of 37 and 45?
What is the GCF of 100 and 114?