Find Greatest Common Divisor of 972 and 783, using Euclidean algorithm.

Answer

The GCD of given numbers is 27.

Step 1 :
Divide $ 972 $ by $ 783 $ and get the remainder

$$ 972 : 783 = 1 \text{ ( remainder is } \color{blue}{ 189 } \text{ ) } $$

The remainder is positive ($ 189 > 0 $), so we will continue with division.

Step 2 :
Divide $ 783 $ by $ \color{blue}{ 189 } $ and get the remainder

$$ 783 : 189 = 4 \text{ ( remainder is } \color{blue}{ 27 } \text{ ) } $$

The remainder is still positive ($ 27 > 0 $), so we will continue with division.

Step 3 :
Divide $ 189 $ by $ \color{blue}{ 27 } $ and get the remainder

$$ 189 : \color{blue}{ \boxed { 27 }} = 7 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 27 }} $.

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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