MATH SOLVE

1 month ago

Q:
# What is the GCF of 13 and 52?

Accepted Solution

A:

Solution: The GCF of 13 and 52 is 13
Methods
How to find the GCF of 13 and 52 using Prime Factorization
One way to find the GCF of 13 and 52 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 13?
What are the Factors of 52?
Here is the prime factorization of 13:
1
3
1
13^1
1 3 1
And this is the prime factorization of 52:
2
2
×
1
3
1
2^2 × 13^1
2 2 × 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 13 and 52 by multiplying all the matching prime factors to get a GCF of 13 and 52 as 169:
Thus, the GCF of 13 and 52 is: 169
How to Find the GCF of 13 and 52 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 13 and 52 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, 13 and 52:
Factors of 13: 1, 13
Factors of 52: 1, 2, 4, 13, 26, 52
When you compare the two lists of factors, you can see that the common factor(s) are 1, 13. Since 13 is the largest of these common factors, the GCF of 13 and 52 would be 13.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 6 and 36?
What is the GCF of 72 and 82?
What is the GCF of 143 and 76?
What is the GCF of 39 and 102?
What is the GCF of 59 and 125?