Find Greatest Common Divisor of 203 and 833, using Euclidean algorithm.
Answer
The GCD of given numbers is 7.
Explanation
Step 1 :
Divide $ 833 $ by $ 203 $ and get the remainder
The remainder is positive ($ 21 > 0 $), so we will continue with division.
Step 2 :
Divide $ 203 $ by $ \color{blue}{ 21 } $ and get the remainder
The remainder is still positive ($ 14 > 0 $), so we will continue with division.
Step 3 :
Divide $ 21 $ by $ \color{blue}{ 14 } $ and get the remainder
The remainder is still positive ($ 7 > 0 $), so we will continue with division.
Step 4 :
Divide $ 14 $ by $ \color{blue}{ 7 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 7 }} $.
We can summarize an algorithm into a following table.
| 833 | : | 203 | = | 4 | remainder ( 21 ) | ||||||
| 203 | : | 21 | = | 9 | remainder ( 14 ) | ||||||
| 21 | : | 14 | = | 1 | remainder ( 7 ) | ||||||
| 14 | : | 7 | = | 2 | remainder ( 0 ) | ||||||
| GCD = 7 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.