Solution: The GCF of 105 and 2 is 1
Methods
How to find the GCF of 105 and 2 using Prime Factorization
One way to find the GCF of 105 and 2 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 2?
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 2:
2
1
2^1
2 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 2 is 1.
Thus, the GCF of 105 and 2 is: 1
How to Find the GCF of 105 and 2 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 105 and 2 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 2:
Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105
Factors of 2: 1, 2
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 2 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 36 and 148?
What is the GCF of 104 and 56?
What is the GCF of 83 and 33?
What is the GCF of 12 and 15?
What is the GCF of 136 and 149?