Solution: The GCF of 84 and 123 is 3
Methods
How to find the GCF of 84 and 123 using Prime Factorization
One way to find the GCF of 84 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 84?
What are the Factors of 123?
Here is the prime factorization of 84:
2
2
×
3
1
×
7
1
2^2 × 3^1 × 7^1
2 2 × 3 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 84 and 123 by multiplying all the matching prime factors to get a GCF of 84 and 123 as 9:
Thus, the GCF of 84 and 123 is: 9
How to Find the GCF of 84 and 123 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 84 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, 84 and 123:
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
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 84 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 88 and 92?
What is the GCF of 61 and 47?
What is the GCF of 104 and 93?
What is the GCF of 70 and 127?
What is the GCF of 114 and 58?