Greatest Common Factor of 100 and 270
GCF(100, 270) = 10, Greatest common factor of 100 and 270 is 10. 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 100 and 270. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 100 and 270 by prime factorization method
We will first find the prime factorization of 100 and 270.
Prime Factorization of 100 is 1, 2, 2, 5, 5 and Prime Factorization of 270 is 1, 2, 3, 3, 3, 5.
- Factorize\( (100) = \) \(1\times 2\times 2\times 5\times 5\)
- Factorize\( (270) = \) \(1\times 2\times 3\times 3\times 3\times 5\)
Now we need to find any which are common for each number (1, 2, 5) and multiply these numbers together.
\(GCF(100, 270) = 1\times 2\times 5 = 10\).
Greatest Common Factor of 100 and 270 by matching factors method
List of positive integers factors of 100 leaving a remainder zero is 1, 2, 4, 5, 10, 20, 25, 50, 100
List of positive integers factors of 270 leaving a remainder zero is 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270
As you can see, 10 is the greatest and common number that 100 and 270 divides into.
So the greatest common factor 100 and 270 is 10.
\(GCF(100, 270) = 10\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
