MATH SOLVE

4 months ago

Q:
# What is the GCF of 104 and 114?

Accepted Solution

A:

Solution: The GCF of 104 and 114 is 2
Methods
How to find the GCF of 104 and 114 using Prime Factorization
One way to find the GCF of 104 and 114 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 104?
What are the Factors of 114?
Here is the prime factorization of 104:
2
3
×
1
3
1
2^3 × 13^1
2 3 × 1 3 1
And this is the prime factorization of 114:
2
1
×
3
1
×
1
9
1
2^1 × 3^1 × 19^1
2 1 × 3 1 × 1 9 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 104 and 114 by multiplying all the matching prime factors to get a GCF of 104 and 114 as 4:
Thus, the GCF of 104 and 114 is: 4
How to Find the GCF of 104 and 114 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 104 and 114 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, 104 and 114:
Factors of 104: 1, 2, 4, 8, 13, 26, 52, 104
Factors of 114: 1, 2, 3, 6, 19, 38, 57, 114
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 104 and 114 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 31 and 71?
What is the GCF of 144 and 72?
What is the GCF of 42 and 103?
What is the GCF of 56 and 45?
What is the GCF of 47 and 113?