Find Greatest Common Divisor of 507885 and 60808, using Euclidean algorithm.
Answer
The GCD of given numbers is 691.
Explanation
Step 1 :
Divide $ 507885 $ by $ 60808 $ and get the remainder
The remainder is positive ($ 21421 > 0 $), so we will continue with division.
Step 2 :
Divide $ 60808 $ by $ \color{blue}{ 21421 } $ and get the remainder
The remainder is still positive ($ 17966 > 0 $), so we will continue with division.
Step 3 :
Divide $ 21421 $ by $ \color{blue}{ 17966 } $ and get the remainder
The remainder is still positive ($ 3455 > 0 $), so we will continue with division.
Step 4 :
Divide $ 17966 $ by $ \color{blue}{ 3455 } $ and get the remainder
The remainder is still positive ($ 691 > 0 $), so we will continue with division.
Step 5 :
Divide $ 3455 $ by $ \color{blue}{ 691 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 691 }} $.
We can summarize an algorithm into a following table.
| 507885 | : | 60808 | = | 8 | remainder ( 21421 ) | ||||||||
| 60808 | : | 21421 | = | 2 | remainder ( 17966 ) | ||||||||
| 21421 | : | 17966 | = | 1 | remainder ( 3455 ) | ||||||||
| 17966 | : | 3455 | = | 5 | remainder ( 691 ) | ||||||||
| 3455 | : | 691 | = | 5 | remainder ( 0 ) | ||||||||
| GCD = 691 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.