Greatest Common Factor of 240 and 1696
GCF(240, 1696) = 16, Greatest common factor of 240 and 1696 is 16. 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 240 and 1696. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 240 and 1696 by prime factorization method
We will first find the prime factorization of 240 and 1696.
Prime Factorization of 240 is 1, 2, 2, 2, 2, 3, 5 and Prime Factorization of 1696 is 1, 2, 2, 2, 2, 2, 53.
- Factorize\( (240) = \) \(1\times 2\times 2\times 2\times 2\times 3\times 5\)
- Factorize\( (1696) = \) \(1\times 2\times 2\times 2\times 2\times 2\times 53\)
Now we need to find any which are common for each number (1, 2, 2, 2, 2) and multiply these numbers together.
\(GCF(240, 1696) = 1\times 2\times 2\times 2\times 2 = 16\).
Greatest Common Factor of 240 and 1696 by matching factors method
List of positive integers factors of 240 leaving a remainder zero is 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
List of positive integers factors of 1696 leaving a remainder zero is 1, 2, 4, 8, 16, 32, 53, 106, 212, 424, 848, 1696
As you can see, 16 is the greatest and common number that 240 and 1696 divides into.
So the greatest common factor 240 and 1696 is 16.
\(GCF(240, 1696) = 16\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
