Greatest Common Factor of 256 and 180
GCF(256, 180) = 4, Greatest common factor of 256 and 180 is 4. 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 256 and 180. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 256 and 180 by prime factorization method
We will first find the prime factorization of 256 and 180.
Prime Factorization of 256 is 1, 2, 2, 2, 2, 2, 2, 2, 2 and Prime Factorization of 180 is 1, 2, 2, 3, 3, 5.
- Factorize\( (256) = \) \(1\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\)
- 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) and multiply these numbers together.
\(GCF(256, 180) = 1\times 2\times 2 = 4\).
Greatest Common Factor of 256 and 180 by matching factors method
List of positive integers factors of 256 leaving a remainder zero is 1, 2, 4, 8, 16, 32, 64, 128, 256
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, 4 is the greatest and common number that 256 and 180 divides into.
So the greatest common factor 256 and 180 is 4.
\(GCF(256, 180) = 4\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
