Find Greatest Common Divisor of 2024 and 1058, using Euclidean algorithm.
Answer
The GCD of given numbers is 46.
Explanation
Step 1 :
Divide $ 2024 $ by $ 1058 $ and get the remainder
The remainder is positive ($ 966 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1058 $ by $ \color{blue}{ 966 } $ and get the remainder
The remainder is still positive ($ 92 > 0 $), so we will continue with division.
Step 3 :
Divide $ 966 $ by $ \color{blue}{ 92 } $ and get the remainder
The remainder is still positive ($ 46 > 0 $), so we will continue with division.
Step 4 :
Divide $ 92 $ by $ \color{blue}{ 46 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 46 }} $.
We can summarize an algorithm into a following table.
| 2024 | : | 1058 | = | 1 | remainder ( 966 ) | ||||||
| 1058 | : | 966 | = | 1 | remainder ( 92 ) | ||||||
| 966 | : | 92 | = | 10 | remainder ( 46 ) | ||||||
| 92 | : | 46 | = | 2 | remainder ( 0 ) | ||||||
| GCD = 46 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.