Solution: The GCF of 35 and 122 is 1
Methods
How to find the GCF of 35 and 122 using Prime Factorization
One way to find the GCF of 35 and 122 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 35?
What are the Factors of 122?
Here is the prime factorization of 35:
5
1
×
7
1
5^1 × 7^1
5 1 × 7 1
And this is the prime factorization of 122:
2
1
×
6
1
1
2^1 × 61^1
2 1 × 6 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 35 and 122 is 1.
Thus, the GCF of 35 and 122 is: 1
How to Find the GCF of 35 and 122 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 35 and 122 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, 35 and 122:
Factors of 35: 1, 5, 7, 35
Factors of 122: 1, 2, 61, 122
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 35 and 122 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 95 and 148?
What is the GCF of 145 and 37?
What is the GCF of 73 and 19?
What is the GCF of 89 and 138?
What is the GCF of 80 and 77?