Greatest Common Factor of 28 and 540
GCF(28, 540) = 4, Greatest common factor of 28 and 540 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 28 and 540. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 28 and 540 by prime factorization method
We will first find the prime factorization of 28 and 540.
Prime Factorization of 28 is 1, 2, 2, 7 and Prime Factorization of 540 is 1, 2, 2, 3, 3, 3, 5.
- Factorize\( (28) = \) \(1\times 2\times 2\times 7\)
- Factorize\( (540) = \) \(1\times 2\times 2\times 3\times 3\times 3\times 5\)
Now we need to find any which are common for each number (1, 2, 2) and multiply these numbers together.
\(GCF(28, 540) = 1\times 2\times 2 = 4\).
Greatest Common Factor of 28 and 540 by matching factors method
List of positive integers factors of 28 leaving a remainder zero is 1, 2, 4, 7, 14, 28
List of positive integers factors of 540 leaving a remainder zero is 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540
As you can see, 4 is the greatest and common number that 28 and 540 divides into.
So the greatest common factor 28 and 540 is 4.
\(GCF(28, 540) = 4\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
