Find Greatest Common Divisor of 2040 and 1368, using Euclidean algorithm.

Answer

The GCD of given numbers is 24.

Step 1 :
Divide $ 2040 $ by $ 1368 $ and get the remainder

$$ 2040 : 1368 = 1 \text{ ( remainder is } \color{blue}{ 672 } \text{ ) } $$

The remainder is positive ($ 672 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1368 $ by $ \color{blue}{ 672 } $ and get the remainder

$$ 1368 : 672 = 2 \text{ ( remainder is } \color{blue}{ 24 } \text{ ) } $$

The remainder is still positive ($ 24 > 0 $), so we will continue with division.

Step 3 :
Divide $ 672 $ by $ \color{blue}{ 24 } $ and get the remainder

$$ 672 : \color{blue}{ \boxed { 24 }} = 28 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 24 }} $.

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

The GCD equals the product of the numbers at the intersection.

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