Solution: The GCF of 68 and 63 is 1
Methods
How to find the GCF of 68 and 63 using Prime Factorization
One way to find the GCF of 68 and 63 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 68?
What are the Factors of 63?
Here is the prime factorization of 68:
2
2
×
1
7
1
2^2 × 17^1
2 2 × 1 7 1
And this is the prime factorization of 63:
3
2
×
7
1
3^2 × 7^1
3 2 × 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 68 and 63 is 1.
Thus, the GCF of 68 and 63 is: 1
How to Find the GCF of 68 and 63 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 68 and 63 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, 68 and 63:
Factors of 68: 1, 2, 4, 17, 34, 68
Factors of 63: 1, 3, 7, 9, 21, 63
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 68 and 63 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 12 and 80?
What is the GCF of 56 and 6?
What is the GCF of 13 and 97?
What is the GCF of 114 and 113?
What is the GCF of 137 and 129?