The GCD of given numbers is 12.
Step 1 :
Divide $ 3612 $ by $ 816 $ and get the remainder
The remainder is positive ($ 348 > 0 $), so we will continue with division.
Step 2 :
Divide $ 816 $ by $ \color{blue}{ 348 } $ and get the remainder
The remainder is still positive ($ 120 > 0 $), so we will continue with division.
Step 3 :
Divide $ 348 $ by $ \color{blue}{ 120 } $ and get the remainder
The remainder is still positive ($ 108 > 0 $), so we will continue with division.
Step 4 :
Divide $ 120 $ by $ \color{blue}{ 108 } $ and get the remainder
The remainder is still positive ($ 12 > 0 $), so we will continue with division.
Step 5 :
Divide $ 108 $ 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.
3612 | : | 816 | = | 4 | remainder ( 348 ) | ||||||||
816 | : | 348 | = | 2 | remainder ( 120 ) | ||||||||
348 | : | 120 | = | 2 | remainder ( 108 ) | ||||||||
120 | : | 108 | = | 1 | remainder ( 12 ) | ||||||||
108 | : | 12 | = | 9 | remainder ( 0 ) | ||||||||
GCD = 12 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.