The GCD of given numbers is 24.
Step 1 :
Divide $ 120 $ by $ 72 $ and get the remainder
The remainder is positive ($ 48 > 0 $), so we will continue with division.
Step 2 :
Divide $ 72 $ by $ \color{blue}{ 48 } $ and get the remainder
The remainder is still positive ($ 24 > 0 $), so we will continue with division.
Step 3 :
Divide $ 48 $ by $ \color{blue}{ 24 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 24 }} $.
We can summarize an algorithm into a following table.
120 | : | 72 | = | 1 | remainder ( 48 ) | ||||
72 | : | 48 | = | 1 | remainder ( 24 ) | ||||
48 | : | 24 | = | 2 | remainder ( 0 ) | ||||
GCD = 24 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.