Greatest Common Factor of 20 and 400
GCF(20, 400) = 20, Greatest common factor of 20 and 400 is 20. 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 20 and 400. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 20 and 400 by prime factorization method
We will first find the prime factorization of 20 and 400.
Prime Factorization of 20 is 1, 2, 2, 5 and Prime Factorization of 400 is 1, 2, 2, 2, 2, 5, 5.
- Factorize\( (20) = \) \(1\times 2\times 2\times 5\)
- Factorize\( (400) = \) \(1\times 2\times 2\times 2\times 2\times 5\times 5\)
Now we need to find any which are common for each number (1, 2, 2, 5) and multiply these numbers together.
\(GCF(20, 400) = 1\times 2\times 2\times 5 = 20\).
Greatest Common Factor of 20 and 400 by matching factors method
List of positive integers factors of 20 leaving a remainder zero is 1, 2, 4, 5, 10, 20
List of positive integers factors of 400 leaving a remainder zero is 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
As you can see, 20 is the greatest and common number that 20 and 400 divides into.
So the greatest common factor 20 and 400 is 20.
\(GCF(20, 400) = 20\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
