Solution: The GCF of 34 and 78 is 2
Methods
How to find the GCF of 34 and 78 using Prime Factorization
One way to find the GCF of 34 and 78 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 78?
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 78:
2
1
×
3
1
×
1
3
1
2^1 × 3^1 × 13^1
2 1 × 3 1 × 1 3 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 34 and 78 by multiplying all the matching prime factors to get a GCF of 34 and 78 as 4:
Thus, the GCF of 34 and 78 is: 4
How to Find the GCF of 34 and 78 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 34 and 78 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 78:
Factors of 34: 1, 2, 17, 34
Factors of 78: 1, 2, 3, 6, 13, 26, 39, 78
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2. Since 2 is the largest of these common factors, the GCF of 34 and 78 would be 2.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 18 and 14?
What is the GCF of 96 and 36?
What is the GCF of 107 and 100?
What is the GCF of 98 and 140?
What is the GCF of 22 and 123?