# Greatest Common Divisor (GCD)

Let you have some cardinal numbers: "a", "b", "c" and you can find one more cardinal number "m", such as you may divide the numbers "a", "b", "c" into the number "m" Then the number "m" is called "divisor" of "a", "b", "c".

##### Example:

Let you have: 14, 6, 8.

You see:

14 ÷ 2 = 7

6 ÷ 2 = 3

8 ÷ 2 = 4

This time, "2" – divisor of 14, 6, 8.

As you can divide every number into "1", then, it's clear, there is always a "divisor" for any numbers.

Let, now your numbers have some divisors, then choose the greatest among them and you'll get the **Greatest Common Divisor (GCD)** for your numbers.

##### Example:

For numbers: 10, 20.

10 = 2 × 5

20 = 2 × 2 × 5

Then "2" – divisor and "5" – divisor, but only "2 × 5" is Greatest Common Divisor for 10 and 20.

GCD = 10.

This example shows you the way to find (GCD). This way is:

- Find all divisors for every number you have.
- Choose the greatest common divisor among them.

##### Example:

Find GCD for 540, 126, 630.

540 = 2 × 2 × 3 × 3 × 3 × 5 = 2^{2} × 3^{3} × 5

126 = 2 × 3 × 3 × 7 = 2 × 3^{2} × 7

630 = 2 × 3 × 3 × 5 × 7 = 2 × 3^{2} × 5 × 7

GCD = 2 × 3 × 3 = 18

### It's interesting

This way for finding (GCD) isn't the only. There is another one, it's named by Euclid.

Now you see, there is nothing difficult here. Moreover, it's interesting to know new things, isn't it?

Read more about "Greatest Common Divisor" and don't forget: "The one who likes to lick the honey must not be afraid of the bees".

#### Note

⁄ - fraction slash

= - is equal to; equals

× - multiplied by

÷ - divided by