Find Greatest Common Divisor of 10234 and 578, using Euclidean algorithm.
Answer
The GCD of given numbers is 34.
Explanation
Step 1 :
Divide $ 10234 $ by $ 578 $ and get the remainder
The remainder is positive ($ 408 > 0 $), so we will continue with division.
Step 2 :
Divide $ 578 $ by $ \color{blue}{ 408 } $ and get the remainder
The remainder is still positive ($ 170 > 0 $), so we will continue with division.
Step 3 :
Divide $ 408 $ by $ \color{blue}{ 170 } $ and get the remainder
The remainder is still positive ($ 68 > 0 $), so we will continue with division.
Step 4 :
Divide $ 170 $ by $ \color{blue}{ 68 } $ and get the remainder
The remainder is still positive ($ 34 > 0 $), so we will continue with division.
Step 5 :
Divide $ 68 $ by $ \color{blue}{ 34 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 34 }} $.
We can summarize an algorithm into a following table.
| 10234 | : | 578 | = | 17 | remainder ( 408 ) | ||||||||
| 578 | : | 408 | = | 1 | remainder ( 170 ) | ||||||||
| 408 | : | 170 | = | 2 | remainder ( 68 ) | ||||||||
| 170 | : | 68 | = | 2 | remainder ( 34 ) | ||||||||
| 68 | : | 34 | = | 2 | remainder ( 0 ) | ||||||||
| GCD = 34 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.