Find Greatest Common Divisor of 2024 and 1446, using Euclidean algorithm.
Answer
The GCD of given numbers is 2.
Explanation
Step 1 :
Divide $ 2024 $ by $ 1446 $ and get the remainder
The remainder is positive ($ 578 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1446 $ by $ \color{blue}{ 578 } $ and get the remainder
The remainder is still positive ($ 290 > 0 $), so we will continue with division.
Step 3 :
Divide $ 578 $ by $ \color{blue}{ 290 } $ and get the remainder
The remainder is still positive ($ 288 > 0 $), so we will continue with division.
Step 4 :
Divide $ 290 $ by $ \color{blue}{ 288 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 5 :
Divide $ 288 $ 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.
| 2024 | : | 1446 | = | 1 | remainder ( 578 ) | ||||||||
| 1446 | : | 578 | = | 2 | remainder ( 290 ) | ||||||||
| 578 | : | 290 | = | 1 | remainder ( 288 ) | ||||||||
| 290 | : | 288 | = | 1 | remainder ( 2 ) | ||||||||
| 288 | : | 2 | = | 144 | remainder ( 0 ) | ||||||||
| GCD = 2 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.