Suppose a integer α(α > 0) and another integer β (β > 0) are given. When α is divided by β we call β is a divisor of α.

For example, 10 has for divisors, 1, 2, 5, and 10.

We can think of a divisor common for two numbers. Suppose 10 and 15 are given. 10 has for divisors, 1, 2, 5, and 10. 15 also has for divisors, 1, 3, 5, and 15. 1 is a common divisor for 10, 15, and 5 is too.

The biggest number of the common divisors, we call it the greatest common divisor(GCD). For 10 and 15, 5 is the GCD.

Here is a calculator for GCD