## Greatest Common Factor of 102 and 160

GCF(102, 160) = 2, Greatest common factor of 102 and 160 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 102 and 160. **Greatest Common Factor by prime factorization method** and **Greatest Common Factor by matching factors method.**

### Greatest Common Factor of 102 and 160 by prime factorization method

We will first find the prime factorization of 102 and 160.

Prime Factorization of 102 is 1, 2, 3, 17 and Prime Factorization of 160 is 1, 2, 2, 2, 2, 2, 5.

- Factorize\( (102) = \) \(1\times 2\times 3\times 17\)
- Factorize\( (160) = \) \(1\times 2\times 2\times 2\times 2\times 2\times 5\)

\(GCF(102, 160) = 1\times 2 = 2\).

### Greatest Common Factor of 102 and 160 by matching factors method

List of positive integers factors of 102 leaving a remainder zero is 1, 2, 3, 6, 17, 34, 51, 102

List of positive integers factors of 160 leaving a remainder zero is 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160

As you can see, 2 is the greatest and common number that 102 and 160 divides into.

So the greatest common factor 102 and 160 is 2.

\(GCF(102, 160) = 2\).