The GCD of given numbers is 72.
Step 1 :
Divide $ 4968 $ by $ 1584 $ and get the remainder
The remainder is positive ($ 216 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1584 $ by $ \color{blue}{ 216 } $ and get the remainder
The remainder is still positive ($ 72 > 0 $), so we will continue with division.
Step 3 :
Divide $ 216 $ by $ \color{blue}{ 72 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 72 }} $.
We can summarize an algorithm into a following table.
4968 | : | 1584 | = | 3 | remainder ( 216 ) | ||||
1584 | : | 216 | = | 7 | remainder ( 72 ) | ||||
216 | : | 72 | = | 3 | remainder ( 0 ) | ||||
GCD = 72 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.