Solution: The GCF of 71 and 2 is 1
Methods
How to find the GCF of 71 and 2 using Prime Factorization
One way to find the GCF of 71 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 71?
What are the Factors of 2?
Here is the prime factorization of 71:
7
1
1
71^1
7 1 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 71 and 2 is 1.
Thus, the GCF of 71 and 2 is: 1
How to Find the GCF of 71 and 2 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 71 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, 71 and 2:
Factors of 71: 1, 71
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 71 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 61 and 125?
What is the GCF of 43 and 67?
What is the GCF of 33 and 104?
What is the GCF of 27 and 70?
What is the GCF of 34 and 7?