Greatest Common Factor of 128 and 1792
GCF(128, 1792) = 128, Greatest common factor of 128 and 1792 is 128. 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 1792. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 128 and 1792 by prime factorization method
We will first find the prime factorization of 128 and 1792.
Prime Factorization of 128 is 1, 2, 2, 2, 2, 2, 2, 2 and Prime Factorization of 1792 is 1, 2, 2, 2, 2, 2, 2, 2, 2, 7.
- Factorize\( (128) = \) \(1\times 2\times 2\times 2\times 2\times 2\times 2\times 2\)
- Factorize\( (1792) = \) \(1\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 7\)
Now we need to find any which are common for each number (1, 2, 2, 2, 2, 2, 2, 2) and multiply these numbers together.
\(GCF(128, 1792) = 1\times 2\times 2\times 2\times 2\times 2\times 2\times 2 = 128\).
Greatest Common Factor of 128 and 1792 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 1792 leaving a remainder zero is 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 256, 448, 896, 1792
As you can see, 128 is the greatest and common number that 128 and 1792 divides into.
So the greatest common factor 128 and 1792 is 128.
\(GCF(128, 1792) = 128\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
