Solution: The GCF of 17 and 68 is 17
Methods
How to find the GCF of 17 and 68 using Prime Factorization
One way to find the GCF of 17 and 68 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 17?
What are the Factors of 68?
Here is the prime factorization of 17:
1
7
1
17^1
1 7 1
And this is the prime factorization of 68:
2
2
×
1
7
1
2^2 × 17^1
2 2 × 1 7 1
When you compare the prime factorization of these two numbers, you can see that there are matching prime factors. You can now find the Greatest Common Factor of 17 and 68 by multiplying all the matching prime factors to get a GCF of 17 and 68 as 289:
Thus, the GCF of 17 and 68 is: 289
How to Find the GCF of 17 and 68 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 17 and 68 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, 17 and 68:
Factors of 17: 1, 17
Factors of 68: 1, 2, 4, 17, 34, 68
When you compare the two lists of factors, you can see that the common factor(s) are 1, 17. Since 17 is the largest of these common factors, the GCF of 17 and 68 would be 17.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 39 and 101?
What is the GCF of 73 and 2?
What is the GCF of 131 and 91?
What is the GCF of 29 and 134?
What is the GCF of 89 and 111?