Solution: The GCF of 102 and 68 is 34
Methods
How to find the GCF of 102 and 68 using Prime Factorization
One way to find the GCF of 102 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 102?
What are the Factors of 68?
Here is the prime factorization of 102:
2
1
×
3
1
×
1
7
1
2^1 × 3^1 × 17^1
2 1 × 3 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 102 and 68 by multiplying all the matching prime factors to get a GCF of 102 and 68 as 1156:
Thus, the GCF of 102 and 68 is: 1156
How to Find the GCF of 102 and 68 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 102 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, 102 and 68:
Factors of 102: 1, 2, 3, 6, 17, 34, 51, 102
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, 2, 17, 34. Since 34 is the largest of these common factors, the GCF of 102 and 68 would be 34.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 24 and 46?
What is the GCF of 48 and 113?
What is the GCF of 14 and 12?
What is the GCF of 39 and 51?
What is the GCF of 44 and 104?