The GCD of given numbers is 23.
Step 1 :
Divide $ 276 $ by $ 115 $ and get the remainder
The remainder is positive ($ 46 > 0 $), so we will continue with division.
Step 2 :
Divide $ 115 $ by $ \color{blue}{ 46 } $ and get the remainder
The remainder is still positive ($ 23 > 0 $), so we will continue with division.
Step 3 :
Divide $ 46 $ by $ \color{blue}{ 23 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 23 }} $.
We can summarize an algorithm into a following table.
276 | : | 115 | = | 2 | remainder ( 46 ) | ||||
115 | : | 46 | = | 2 | remainder ( 23 ) | ||||
46 | : | 23 | = | 2 | remainder ( 0 ) | ||||
GCD = 23 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.