Find Greatest Common Divisor of 36 and 54, using Euclidean algorithm.
Answer
The GCD of given numbers is 18.
Explanation
Step 1 :
Divide $ 54 $ by $ 36 $ and get the remainder
The remainder is positive ($ 18 > 0 $), so we will continue with division.
Step 2 :
Divide $ 36 $ by $ \color{blue}{ 18 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 18 }} $.
We can summarize an algorithm into a following table.
| 54 | : | 36 | = | 1 | remainder ( 18 ) | ||
| 36 | : | 18 | = | 2 | remainder ( 0 ) | ||
| GCD = 18 | |||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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