The GCD of given numbers is 3.
Step 1 :
Divide $ 1461 $ by $ 117 $ and get the remainder
The remainder is positive ($ 57 > 0 $), so we will continue with division.
Step 2 :
Divide $ 117 $ by $ \color{blue}{ 57 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 3 :
Divide $ 57 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 3 }} $.
We can summarize an algorithm into a following table.
1461 | : | 117 | = | 12 | remainder ( 57 ) | ||||
117 | : | 57 | = | 2 | remainder ( 3 ) | ||||
57 | : | 3 | = | 19 | remainder ( 0 ) | ||||
GCD = 3 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.