Greatest Common Factor of 128 and 1680
GCF(128, 1680) = 16, Greatest common factor of 128 and 1680 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 128 and 1680. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 128 and 1680 by prime factorization method
We will first find the prime factorization of 128 and 1680.
Prime Factorization of 128 is 1, 2, 2, 2, 2, 2, 2, 2 and Prime Factorization of 1680 is 1, 2, 2, 2, 2, 3, 5, 7.
- Factorize\( (128) = \) \(1\times 2\times 2\times 2\times 2\times 2\times 2\times 2\)
- Factorize\( (1680) = \) \(1\times 2\times 2\times 2\times 2\times 3\times 5\times 7\)
Now we need to find any which are common for each number (1, 2, 2, 2, 2) and multiply these numbers together.
\(GCF(128, 1680) = 1\times 2\times 2\times 2\times 2 = 16\).
Greatest Common Factor of 128 and 1680 by matching factors method
List of positive integers factors of 128 leaving a remainder zero is 1, 2, 4, 8, 16, 32, 64, 128
List of positive integers factors of 1680 leaving a remainder zero is 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 112, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840, 1680
As you can see, 16 is the greatest and common number that 128 and 1680 divides into.
So the greatest common factor 128 and 1680 is 16.
\(GCF(128, 1680) = 16\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
