Solution: The GCF of 144 and 69 is 3
Methods
How to find the GCF of 144 and 69 using Prime Factorization
One way to find the GCF of 144 and 69 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 144?
What are the Factors of 69?
Here is the prime factorization of 144:
2
4
×
3
2
2^4 × 3^2
2 4 × 3 2
And this is the prime factorization of 69:
3
1
×
2
3
1
3^1 × 23^1
3 1 × 2 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 144 and 69 by multiplying all the matching prime factors to get a GCF of 144 and 69 as 9:
Thus, the GCF of 144 and 69 is: 9
How to Find the GCF of 144 and 69 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 144 and 69 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, 144 and 69:
Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Factors of 69: 1, 3, 23, 69
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 144 and 69 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 100 and 23?
What is the GCF of 69 and 61?
What is the GCF of 83 and 63?
What is the GCF of 57 and 44?
What is the GCF of 146 and 31?