Solution: The GCF of 48 and 129 is 3
Methods
How to find the GCF of 48 and 129 using Prime Factorization
One way to find the GCF of 48 and 129 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 48?
What are the Factors of 129?
Here is the prime factorization of 48:
2
4
×
3
1
2^4 × 3^1
2 4 × 3 1
And this is the prime factorization of 129:
3
1
×
4
3
1
3^1 × 43^1
3 1 × 4 3 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 48 and 129 by multiplying all the matching prime factors to get a GCF of 48 and 129 as 9:
Thus, the GCF of 48 and 129 is: 9
How to Find the GCF of 48 and 129 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 48 and 129 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, 48 and 129:
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 129: 1, 3, 43, 129
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 48 and 129 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 21 and 104?
What is the GCF of 54 and 85?
What is the GCF of 143 and 147?
What is the GCF of 55 and 37?
What is the GCF of 45 and 66?