MATH SOLVE

3 months ago

Q:
# What is the GCF of 147 and 58?

Accepted Solution

A:

Solution: The GCF of 147 and 58 is 1
Methods
How to find the GCF of 147 and 58 using Prime Factorization
One way to find the GCF of 147 and 58 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 147?
What are the Factors of 58?
Here is the prime factorization of 147:
3
1
×
7
2
3^1 × 7^2
3 1 × 7 2
And this is the prime factorization of 58:
2
1
×
2
9
1
2^1 × 29^1
2 1 × 2 9 1
When you compare the prime factorization of these two numbers, you can see that there are no matching prime factors. When this is the case, it means that there are no common factors between these two numbers. As a result, the GCF of 147 and 58 is 1.
Thus, the GCF of 147 and 58 is: 1
How to Find the GCF of 147 and 58 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 147 and 58 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, 147 and 58:
Factors of 147: 1, 3, 7, 21, 49, 147
Factors of 58: 1, 2, 29, 58
When you compare the two lists of factors, you can see that the only common factor is 1. So, in this case, the GCF of 147 and 58 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 30 and 56?
What is the GCF of 43 and 138?
What is the GCF of 120 and 27?
What is the GCF of 20 and 80?
What is the GCF of 40 and 16?