MATH SOLVE

1 month ago

Q:
# What is the GCF of 150 and 99?

Accepted Solution

A:

Solution: The GCF of 150 and 99 is 3
Methods
How to find the GCF of 150 and 99 using Prime Factorization
One way to find the GCF of 150 and 99 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 150?
What are the Factors of 99?
Here is the prime factorization of 150:
2
1
Γ
3
1
Γ
5
2
2^1 Γ 3^1 Γ 5^2
2 1 Γ 3 1 Γ 5 2
And this is the prime factorization of 99:
3
2
Γ
1
1
1
3^2 Γ 11^1
3 2 Γ 1 1 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 150 and 99 by multiplying all the matching prime factors to get a GCF of 150 and 99 as 9:
Thus, the GCF of 150 and 99 is: 9
How to Find the GCF of 150 and 99 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 150 and 99 is to find and list all the factors of each number. Again, you can see how this is done by looking at the βFactors ofβ articles that are linked to above.
Letβs take a look at the factors for each of these numbers, 150 and 99:
Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
Factors of 99: 1, 3, 9, 11, 33, 99
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 150 and 99 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 107 and 33?
What is the GCF of 131 and 103?
What is the GCF of 113 and 93?
What is the GCF of 14 and 35?
What is the GCF of 81 and 84?