Solution: The GCF of 34 and 21 is 1
Methods
How to find the GCF of 34 and 21 using Prime Factorization
One way to find the GCF of 34 and 21 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 34?
What are the Factors of 21?
Here is the prime factorization of 34:
2
1
×
1
7
1
2^1 × 17^1
2 1 × 1 7 1
And this is the prime factorization of 21:
3
1
×
7
1
3^1 × 7^1
3 1 × 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 34 and 21 is 1.
Thus, the GCF of 34 and 21 is: 1
How to Find the GCF of 34 and 21 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 34 and 21 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, 34 and 21:
Factors of 34: 1, 2, 17, 34
Factors of 21: 1, 3, 7, 21
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 34 and 21 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 115 and 76?
What is the GCF of 44 and 56?
What is the GCF of 147 and 41?
What is the GCF of 42 and 68?
What is the GCF of 12 and 27?