Greatest Common Factor of 144 and 128
GCF(144, 128) = 16, Greatest common factor of 144 and 128 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 144 and 128. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 144 and 128 by prime factorization method
We will first find the prime factorization of 144 and 128.
Prime Factorization of 144 is 1, 2, 2, 2, 2, 3, 3 and Prime Factorization of 128 is 1, 2, 2, 2, 2, 2, 2, 2.
- Factorize\( (144) = \) \(1\times 2\times 2\times 2\times 2\times 3\times 3\)
- Factorize\( (128) = \) \(1\times 2\times 2\times 2\times 2\times 2\times 2\times 2\)
Now we need to find any which are common for each number (1, 2, 2, 2, 2) and multiply these numbers together.
\(GCF(144, 128) = 1\times 2\times 2\times 2\times 2 = 16\).
Greatest Common Factor of 144 and 128 by matching factors method
List of positive integers factors of 144 leaving a remainder zero is 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
List of positive integers factors of 128 leaving a remainder zero is 1, 2, 4, 8, 16, 32, 64, 128
As you can see, 16 is the greatest and common number that 144 and 128 divides into.
So the greatest common factor 144 and 128 is 16.
\(GCF(144, 128) = 16\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
