MATH SOLVE

3 months ago

Q:
# What is the GCF of 123 and 147?

Accepted Solution

A:

Solution: The GCF of 123 and 147 is 3
Methods
How to find the GCF of 123 and 147 using Prime Factorization
One way to find the GCF of 123 and 147 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 123?
What are the Factors of 147?
Here is the prime factorization of 123:
3
1
×
4
1
1
3^1 × 41^1
3 1 × 4 1 1
And this is the prime factorization of 147:
3
1
×
7
2
3^1 × 7^2
3 1 × 7 2
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 123 and 147 by multiplying all the matching prime factors to get a GCF of 123 and 147 as 9:
Thus, the GCF of 123 and 147 is: 9
How to Find the GCF of 123 and 147 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 123 and 147 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, 123 and 147:
Factors of 123: 1, 3, 41, 123
Factors of 147: 1, 3, 7, 21, 49, 147
When you compare the two lists of factors, you can see that the common factor(s) are 1, 3. Since 3 is the largest of these common factors, the GCF of 123 and 147 would be 3.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 3 and 113?
What is the GCF of 78 and 83?
What is the GCF of 136 and 92?
What is the GCF of 51 and 49?
What is the GCF of 5 and 60?