MATH SOLVE

3 months ago

Q:
# What is the GCF of 100 and 134?

Accepted Solution

A:

Solution: The GCF of 100 and 134 is 2
Methods
How to find the GCF of 100 and 134 using Prime Factorization
One way to find the GCF of 100 and 134 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 100?
What are the Factors of 134?
Here is the prime factorization of 100:
2
2
×
5
2
2^2 × 5^2
2 2 × 5 2
And this is the prime factorization of 134:
2
1
×
6
7
1
2^1 × 67^1
2 1 × 6 7 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 100 and 134 by multiplying all the matching prime factors to get a GCF of 100 and 134 as 4:
Thus, the GCF of 100 and 134 is: 4
How to Find the GCF of 100 and 134 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 100 and 134 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, 100 and 134:
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
Factors of 134: 1, 2, 67, 134
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 100 and 134 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 60 and 148?
What is the GCF of 122 and 149?
What is the GCF of 59 and 44?
What is the GCF of 78 and 35?
What is the GCF of 48 and 81?