Find Greatest Common Divisor of 11391 and 5673, using Euclidean algorithm.

Answer

The GCD of given numbers is 3.

Step 1 :
Divide $ 11391 $ by $ 5673 $ and get the remainder

$$ 11391 : 5673 = 2 \text{ ( remainder is } \color{blue}{ 45 } \text{ ) } $$

The remainder is positive ($ 45 > 0 $), so we will continue with division.

Step 2 :
Divide $ 5673 $ by $ \color{blue}{ 45 } $ and get the remainder

$$ 5673 : 45 = 126 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

The remainder is still positive ($ 3 > 0 $), so we will continue with division.

Step 3 :
Divide $ 45 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 45 : \color{blue}{ \boxed { 3 }} = 15 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 3 }} $.

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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