## Greatest Common Factor of 30 and 128

GCF(30, 128) = 2, Greatest common factor of 30 and 128 is 2. 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 30 and 128. **Greatest Common Factor by prime factorization method** and **Greatest Common Factor by matching factors method.**

### Greatest Common Factor of 30 and 128 by prime factorization method

We will first find the prime factorization of 30 and 128.

Prime Factorization of 30 is 1, 2, 3, 5 and Prime Factorization of 128 is 1, 2, 2, 2, 2, 2, 2, 2.

- Factorize\( (30) = \) \(1\times 2\times 3\times 5\)
- Factorize\( (128) = \) \(1\times 2\times 2\times 2\times 2\times 2\times 2\times 2\)

\(GCF(30, 128) = 1\times 2 = 2\).

### Greatest Common Factor of 30 and 128 by matching factors method

List of positive integers factors of 30 leaving a remainder zero is 1, 2, 3, 5, 6, 10, 15, 30

List of positive integers factors of 128 leaving a remainder zero is 1, 2, 4, 8, 16, 32, 64, 128

As you can see, 2 is the greatest and common number that 30 and 128 divides into.

So the greatest common factor 30 and 128 is 2.

\(GCF(30, 128) = 2\).