Solution: The GCF of 70 and 111 is 1
Methods
How to find the GCF of 70 and 111 using Prime Factorization
One way to find the GCF of 70 and 111 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 70?
What are the Factors of 111?
Here is the prime factorization of 70:
2
1
×
5
1
×
7
1
2^1 × 5^1 × 7^1
2 1 × 5 1 × 7 1
And this is the prime factorization of 111:
3
1
×
3
7
1
3^1 × 37^1
3 1 × 3 7 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 70 and 111 is 1.
Thus, the GCF of 70 and 111 is: 1
How to Find the GCF of 70 and 111 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 70 and 111 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, 70 and 111:
Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70
Factors of 111: 1, 3, 37, 111
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 70 and 111 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 72?
What is the GCF of 91 and 76?
What is the GCF of 146 and 44?
What is the GCF of 148 and 54?
What is the GCF of 137 and 39?