Find Greatest Common Divisor of 816 and 1071, using Euclidean algorithm.

Answer

The GCD of given numbers is 51.

Step 1 :
Divide $ 1071 $ by $ 816 $ and get the remainder

$$ 1071 : 816 = 1 \text{ ( remainder is } \color{blue}{ 255 } \text{ ) } $$

The remainder is positive ($ 255 > 0 $), so we will continue with division.

Step 2 :
Divide $ 816 $ by $ \color{blue}{ 255 } $ and get the remainder

$$ 816 : 255 = 3 \text{ ( remainder is } \color{blue}{ 51 } \text{ ) } $$

The remainder is still positive ($ 51 > 0 $), so we will continue with division.

Step 3 :
Divide $ 255 $ by $ \color{blue}{ 51 } $ and get the remainder

$$ 255 : \color{blue}{ \boxed { 51 }} = 5 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 51 }} $.

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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