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

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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.

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