Find Greatest Common Divisor of 13113 and 1410, using Euclidean algorithm.

Answer

The GCD of given numbers is 141.

Step 1 :
Divide $ 13113 $ by $ 1410 $ and get the remainder

$$ 13113 : 1410 = 9 \text{ ( remainder is } \color{blue}{ 423 } \text{ ) } $$

The remainder is positive ($ 423 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1410 $ by $ \color{blue}{ 423 } $ and get the remainder

$$ 1410 : 423 = 3 \text{ ( remainder is } \color{blue}{ 141 } \text{ ) } $$

The remainder is still positive ($ 141 > 0 $), so we will continue with division.

Step 3 :
Divide $ 423 $ by $ \color{blue}{ 141 } $ and get the remainder

$$ 423 : \color{blue}{ \boxed { 141 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 141 }} $.

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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