Find Greatest Common Divisor of 1024 and 486, using Euclidean algorithm.
Answer
The GCD of given numbers is 2.
Explanation
Step 1 :
Divide $ 1024 $ by $ 486 $ and get the remainder
The remainder is positive ($ 52 > 0 $), so we will continue with division.
Step 2 :
Divide $ 486 $ by $ \color{blue}{ 52 } $ and get the remainder
The remainder is still positive ($ 18 > 0 $), so we will continue with division.
Step 3 :
Divide $ 52 $ by $ \color{blue}{ 18 } $ and get the remainder
The remainder is still positive ($ 16 > 0 $), so we will continue with division.
Step 4 :
Divide $ 18 $ by $ \color{blue}{ 16 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 5 :
Divide $ 16 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 2 }} $.
We can summarize an algorithm into a following table.
| 1024 | : | 486 | = | 2 | remainder ( 52 ) | ||||||||
| 486 | : | 52 | = | 9 | remainder ( 18 ) | ||||||||
| 52 | : | 18 | = | 2 | remainder ( 16 ) | ||||||||
| 18 | : | 16 | = | 1 | remainder ( 2 ) | ||||||||
| 16 | : | 2 | = | 8 | remainder ( 0 ) | ||||||||
| GCD = 2 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.