greatest common divisor

GCD

A divisor is another name of factor.  A factor is a number which divides a given number completely with leaving a reminder zero.

Let us find all the factors of 10

Number 10 is divided by 1,2,5,10, So these four numbers are the factors of 10.

Let us take another example of 20

Number 20 is divided by 1,2,4,5,10,20

Now we are going to find out the great common divisor of 10,20

let us take all the common factors of 10 & 20

1,2,5,10

Among the common factors of 10 & 20, the greatest number which is factor to both the 10, 20 is 10.

Hence the greatest common divisor of 10, 20 is 10.

The meaning is 10 is only the number which divides equally both 10,20.