Greatest Common Factor of 160 and 4000
GCF(160, 4000) = 160, Greatest common factor of 160 and 4000 is 160. 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 160 and 4000. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 160 and 4000 by prime factorization method
We will first find the prime factorization of 160 and 4000.
Prime Factorization of 160 is 1, 2, 2, 2, 2, 2, 5 and Prime Factorization of 4000 is 1, 2, 2, 2, 2, 2, 5, 5, 5.
- Factorize\( (160) = \) \(1\times 2\times 2\times 2\times 2\times 2\times 5\)
- Factorize\( (4000) = \) \(1\times 2\times 2\times 2\times 2\times 2\times 5\times 5\times 5\)
Now we need to find any which are common for each number (1, 2, 2, 2, 2, 2, 5) and multiply these numbers together.
\(GCF(160, 4000) = 1\times 2\times 2\times 2\times 2\times 2\times 5 = 160\).
Greatest Common Factor of 160 and 4000 by matching factors method
List of positive integers factors of 160 leaving a remainder zero is 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160
List of positive integers factors of 4000 leaving a remainder zero is 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 800, 1000, 2000, 4000
As you can see, 160 is the greatest and common number that 160 and 4000 divides into.
So the greatest common factor 160 and 4000 is 160.
\(GCF(160, 4000) = 160\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
