Find Greatest Common Divisor of 6536 and 9503, using Euclidean algorithm.
Answer
The GCD of given numbers is 43.
Explanation
Step 1 :
Divide $ 9503 $ by $ 6536 $ and get the remainder
The remainder is positive ($ 2967 > 0 $), so we will continue with division.
Step 2 :
Divide $ 6536 $ by $ \color{blue}{ 2967 } $ and get the remainder
The remainder is still positive ($ 602 > 0 $), so we will continue with division.
Step 3 :
Divide $ 2967 $ by $ \color{blue}{ 602 } $ and get the remainder
The remainder is still positive ($ 559 > 0 $), so we will continue with division.
Step 4 :
Divide $ 602 $ by $ \color{blue}{ 559 } $ and get the remainder
The remainder is still positive ($ 43 > 0 $), so we will continue with division.
Step 5 :
Divide $ 559 $ by $ \color{blue}{ 43 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 43 }} $.
We can summarize an algorithm into a following table.
| 9503 | : | 6536 | = | 1 | remainder ( 2967 ) | ||||||||
| 6536 | : | 2967 | = | 2 | remainder ( 602 ) | ||||||||
| 2967 | : | 602 | = | 4 | remainder ( 559 ) | ||||||||
| 602 | : | 559 | = | 1 | remainder ( 43 ) | ||||||||
| 559 | : | 43 | = | 13 | remainder ( 0 ) | ||||||||
| GCD = 43 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.