The GCD of given numbers is 120.
Step 1 :
Divide $ 1800 $ by $ 480 $ and get the remainder
The remainder is positive ($ 360 > 0 $), so we will continue with division.
Step 2 :
Divide $ 480 $ by $ \color{blue}{ 360 } $ and get the remainder
The remainder is still positive ($ 120 > 0 $), so we will continue with division.
Step 3 :
Divide $ 360 $ by $ \color{blue}{ 120 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 120 }} $.
We can summarize an algorithm into a following table.
1800 | : | 480 | = | 3 | remainder ( 360 ) | ||||
480 | : | 360 | = | 1 | remainder ( 120 ) | ||||
360 | : | 120 | = | 3 | remainder ( 0 ) | ||||
GCD = 120 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.