Solution: The GCF of 144 and 40 is 8
Methods
How to find the GCF of 144 and 40 using Prime Factorization
One way to find the GCF of 144 and 40 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 40?
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 40:
2
3
×
5
1
2^3 × 5^1
2 3 × 5 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 40 by multiplying all the matching prime factors to get a GCF of 144 and 40 as 4:
Thus, the GCF of 144 and 40 is: 4
How to Find the GCF of 144 and 40 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 144 and 40 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 40:
Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 4, 8. Since 8 is the largest of these common factors, the GCF of 144 and 40 would be 8.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 62 and 76?
What is the GCF of 31 and 84?
What is the GCF of 146 and 129?
What is the GCF of 1 and 49?
What is the GCF of 142 and 105?