The GCD of given numbers is 12.
Step 1 :
Divide $ 720 $ by $ 588 $ and get the remainder
The remainder is positive ($ 132 > 0 $), so we will continue with division.
Step 2 :
Divide $ 588 $ by $ \color{blue}{ 132 } $ and get the remainder
The remainder is still positive ($ 60 > 0 $), so we will continue with division.
Step 3 :
Divide $ 132 $ by $ \color{blue}{ 60 } $ and get the remainder
The remainder is still positive ($ 12 > 0 $), so we will continue with division.
Step 4 :
Divide $ 60 $ by $ \color{blue}{ 12 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 12 }} $.
We can summarize an algorithm into a following table.
720 | : | 588 | = | 1 | remainder ( 132 ) | ||||||
588 | : | 132 | = | 4 | remainder ( 60 ) | ||||||
132 | : | 60 | = | 2 | remainder ( 12 ) | ||||||
60 | : | 12 | = | 5 | remainder ( 0 ) | ||||||
GCD = 12 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.