Greatest Common Factor of 240 and 180
GCF(240, 180) = 60, Greatest common factor of 240 and 180 is 60. Greatest Common Factor or Greatest Common Divisor of two numbers is the largest integer by which both the numbers can be divided. There are two different methods to calculate Greatest Common Factor of 240 and 180. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 240 and 180 by prime factorization method
We will first find the prime factorization of 240 and 180.
Prime Factorization of 240 is 1, 2, 2, 2, 2, 3, 5 and Prime Factorization of 180 is 1, 2, 2, 3, 3, 5.
- Factorize\( (240) = \) \(1\times 2\times 2\times 2\times 2\times 3\times 5\)
- Factorize\( (180) = \) \(1\times 2\times 2\times 3\times 3\times 5\)
Now we need to find any which are common for each number (1, 2, 2, 3, 5) and multiply these numbers together.
\(GCF(240, 180) = 1\times 2\times 2\times 3\times 5 = 60\).
Greatest Common Factor of 240 and 180 by matching factors method
List of positive integers factors of 240 leaving a remainder zero is 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
List of positive integers factors of 180 leaving a remainder zero is 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
As you can see, 60 is the greatest and common number that 240 and 180 divides into.
So the greatest common factor 240 and 180 is 60.
\(GCF(240, 180) = 60\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
