The GCD of given numbers is 6.
Step 1 :
Divide $ 312 $ by $ 114 $ and get the remainder
The remainder is positive ($ 84 > 0 $), so we will continue with division.
Step 2 :
Divide $ 114 $ by $ \color{blue}{ 84 } $ and get the remainder
The remainder is still positive ($ 30 > 0 $), so we will continue with division.
Step 3 :
Divide $ 84 $ by $ \color{blue}{ 30 } $ and get the remainder
The remainder is still positive ($ 24 > 0 $), so we will continue with division.
Step 4 :
Divide $ 30 $ by $ \color{blue}{ 24 } $ and get the remainder
The remainder is still positive ($ 6 > 0 $), so we will continue with division.
Step 5 :
Divide $ 24 $ by $ \color{blue}{ 6 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 6 }} $.
We can summarize an algorithm into a following table.
312 | : | 114 | = | 2 | remainder ( 84 ) | ||||||||
114 | : | 84 | = | 1 | remainder ( 30 ) | ||||||||
84 | : | 30 | = | 2 | remainder ( 24 ) | ||||||||
30 | : | 24 | = | 1 | remainder ( 6 ) | ||||||||
24 | : | 6 | = | 4 | remainder ( 0 ) | ||||||||
GCD = 6 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.