Greatest Common Factor of 540 and 1305
GCF(540, 1305) = 45, Greatest common factor of 540 and 1305 is 45. 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 540 and 1305. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 540 and 1305 by prime factorization method
We will first find the prime factorization of 540 and 1305.
Prime Factorization of 540 is 1, 2, 2, 3, 3, 3, 5 and Prime Factorization of 1305 is 1, 3, 3, 5, 29.
- Factorize\( (540) = \) \(1\times 2\times 2\times 3\times 3\times 3\times 5\)
- Factorize\( (1305) = \) \(1\times 3\times 3\times 5\times 29\)
Now we need to find any which are common for each number (1, 3, 3, 5) and multiply these numbers together.
\(GCF(540, 1305) = 1\times 3\times 3\times 5 = 45\).
Greatest Common Factor of 540 and 1305 by matching factors method
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
List of positive integers factors of 1305 leaving a remainder zero is 1, 3, 5, 9, 15, 29, 45, 87, 145, 261, 435, 1305
As you can see, 45 is the greatest and common number that 540 and 1305 divides into.
So the greatest common factor 540 and 1305 is 45.
\(GCF(540, 1305) = 45\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
