Find Greatest Common Divisor of 2024 and 112, using Euclidean algorithm.
Answer
The GCD of given numbers is 8.
Explanation
Step 1 :
Divide $ 2024 $ by $ 112 $ and get the remainder
The remainder is positive ($ 8 > 0 $), so we will continue with division.
Step 2 :
Divide $ 112 $ by $ \color{blue}{ 8 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 8 }} $.
We can summarize an algorithm into a following table.
| 2024 | : | 112 | = | 18 | remainder ( 8 ) | ||
| 112 | : | 8 | = | 14 | remainder ( 0 ) | ||
| GCD = 8 | |||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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