What is the greatest common divisor and how to find the greatest common divisor of two numbers.

Greatest common divisor:

                                               The greatest common divisor of  two integers a and b.Which are not both zero is the largest integer that divides both a and b.Which is written as (a,b) and is also written as,

    gcd(a,b)

The  greatest common divisor is a number which should divide the number a and b,Now we find the gcd of some numbers as under.

For example: 

Find the gcd of  24 and 30.

First find the divisors of  24 and 30 

we have.

        24 = 1,2,3,4,6,8,12,24

        30 = 1,2,3,5,6,10,15,30

Now we seen that there are many common divisors of 24 and 30.these are (1,2,3,6) but we have to chose the largest number which is a common divisor of 24 and 30.Here 6 is the largest integer that is the greatest common divisor of both 24 and 30.So 6 is the greatest common divisor of 24 and 30.

Another example:

     find the gcd of    20 and 35.

           Factors of 20 and 35.

20=1,2,4,5,10,20

35=1,5,7,35

So the greatest common divisor of 20 and 35 is 5.