Solution: The GCF of 39 and 78 is 39
Methods
How to find the GCF of 39 and 78 using Prime Factorization
One way to find the GCF of 39 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 39?
What are the Factors of 78?
Here is the prime factorization of 39:
3
1
×
1
3
1
3^1 × 13^1
3 1 × 1 3 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 39 and 78 by multiplying all the matching prime factors to get a GCF of 39 and 78 as 1521:
Thus, the GCF of 39 and 78 is: 1521
How to Find the GCF of 39 and 78 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 39 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, 39 and 78:
Factors of 39: 1, 3, 13, 39
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, 3, 13, 39. Since 39 is the largest of these common factors, the GCF of 39 and 78 would be 39.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 142 and 54?
What is the GCF of 87 and 84?
What is the GCF of 75 and 62?
What is the GCF of 51 and 47?
What is the GCF of 94 and 127?