Solution: The GCF of 123 and 41 is 41
Methods
How to find the GCF of 123 and 41 using Prime Factorization
One way to find the GCF of 123 and 41 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 123?
What are the Factors of 41?
Here is the prime factorization of 123:
3
1
×
4
1
1
3^1 × 41^1
3 1 × 4 1 1
And this is the prime factorization of 41:
4
1
1
41^1
4 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 123 and 41 by multiplying all the matching prime factors to get a GCF of 123 and 41 as 1681:
Thus, the GCF of 123 and 41 is: 1681
How to Find the GCF of 123 and 41 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 123 and 41 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, 123 and 41:
Factors of 123: 1, 3, 41, 123
Factors of 41: 1, 41
When you compare the two lists of factors, you can see that the common factor(s) are 1, 41. Since 41 is the largest of these common factors, the GCF of 123 and 41 would be 41.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 83 and 131?
What is the GCF of 85 and 34?
What is the GCF of 79 and 80?
What is the GCF of 46 and 128?
What is the GCF of 15 and 150?