Solution: The GCF of 102 and 123 is 3
Methods
How to find the GCF of 102 and 123 using Prime Factorization
One way to find the GCF of 102 and 123 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 102?
What are the Factors of 123?
Here is the prime factorization of 102:
2
1
×
3
1
×
1
7
1
2^1 × 3^1 × 17^1
2 1 × 3 1 × 1 7 1
And this is the prime factorization of 123:
3
1
×
4
1
1
3^1 × 41^1
3 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 102 and 123 by multiplying all the matching prime factors to get a GCF of 102 and 123 as 9:
Thus, the GCF of 102 and 123 is: 9
How to Find the GCF of 102 and 123 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 102 and 123 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, 102 and 123:
Factors of 102: 1, 2, 3, 6, 17, 34, 51, 102
Factors of 123: 1, 3, 41, 123
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 102 and 123 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 26 and 50?
What is the GCF of 46 and 16?
What is the GCF of 134 and 111?
What is the GCF of 103 and 113?
What is the GCF of 17 and 115?