Solution: The GCF of 129 and 141 is 3
Methods
How to find the GCF of 129 and 141 using Prime Factorization
One way to find the GCF of 129 and 141 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 129?
What are the Factors of 141?
Here is the prime factorization of 129:
3
1
×
4
3
1
3^1 × 43^1
3 1 × 4 3 1
And this is the prime factorization of 141:
3
1
×
4
7
1
3^1 × 47^1
3 1 × 4 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 129 and 141 by multiplying all the matching prime factors to get a GCF of 129 and 141 as 9:
Thus, the GCF of 129 and 141 is: 9
How to Find the GCF of 129 and 141 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 129 and 141 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, 129 and 141:
Factors of 129: 1, 3, 43, 129
Factors of 141: 1, 3, 47, 141
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 129 and 141 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 150 and 8?
What is the GCF of 99 and 120?
What is the GCF of 105 and 87?
What is the GCF of 11 and 43?
What is the GCF of 61 and 40?