Greatest Common Factor of 40 and 1728
GCF(40, 1728) = 8, Greatest common factor of 40 and 1728 is 8. 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 40 and 1728. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 40 and 1728 by prime factorization method
We will first find the prime factorization of 40 and 1728.
Prime Factorization of 40 is 1, 2, 2, 2, 5 and Prime Factorization of 1728 is 1, 2, 2, 2, 2, 2, 2, 3, 3, 3.
- Factorize\( (40) = \) \(1\times 2\times 2\times 2\times 5\)
- Factorize\( (1728) = \) \(1\times 2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 3\)
Now we need to find any which are common for each number (1, 2, 2, 2) and multiply these numbers together.
\(GCF(40, 1728) = 1\times 2\times 2\times 2 = 8\).
Greatest Common Factor of 40 and 1728 by matching factors method
List of positive integers factors of 40 leaving a remainder zero is 1, 2, 4, 5, 8, 10, 20, 40
List of positive integers factors of 1728 leaving a remainder zero is 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864, 1728
As you can see, 8 is the greatest and common number that 40 and 1728 divides into.
So the greatest common factor 40 and 1728 is 8.
\(GCF(40, 1728) = 8\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
