Solution: The GCF of 33 and 142 is 1
Methods
How to find the GCF of 33 and 142 using Prime Factorization
One way to find the GCF of 33 and 142 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 33?
What are the Factors of 142?
Here is the prime factorization of 33:
3
1
×
1
1
1
3^1 × 11^1
3 1 × 1 1 1
And this is the prime factorization of 142:
2
1
×
7
1
1
2^1 × 71^1
2 1 × 7 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 33 and 142 is 1.
Thus, the GCF of 33 and 142 is: 1
How to Find the GCF of 33 and 142 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 33 and 142 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, 33 and 142:
Factors of 33: 1, 3, 11, 33
Factors of 142: 1, 2, 71, 142
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 33 and 142 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 54 and 24?
What is the GCF of 31 and 64?
What is the GCF of 7 and 148?
What is the GCF of 103 and 60?
What is the GCF of 66 and 109?