Find Greatest Common Divisor of 123 and 451, using Euclidean algorithm.

Answer

The GCD of given numbers is 41.

Step 1 :
Divide $ 451 $ by $ 123 $ and get the remainder

$$ 451 : 123 = 3 \text{ ( remainder is } \color{blue}{ 82 } \text{ ) } $$

The remainder is positive ($ 82 > 0 $), so we will continue with division.

Step 2 :
Divide $ 123 $ by $ \color{blue}{ 82 } $ and get the remainder

$$ 123 : 82 = 1 \text{ ( remainder is } \color{blue}{ 41 } \text{ ) } $$

The remainder is still positive ($ 41 > 0 $), so we will continue with division.

Step 3 :
Divide $ 82 $ by $ \color{blue}{ 41 } $ and get the remainder

$$ 82 : \color{blue}{ \boxed { 41 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 41 }} $.

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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