Find Greatest Common Divisor of 272 and 119, using Euclidean algorithm.

Answer

The GCD of given numbers is 17.

Step 1 :
Divide $ 272 $ by $ 119 $ and get the remainder

$$ 272 : 119 = 2 \text{ ( remainder is } \color{blue}{ 34 } \text{ ) } $$

The remainder is positive ($ 34 > 0 $), so we will continue with division.

Step 2 :
Divide $ 119 $ by $ \color{blue}{ 34 } $ and get the remainder

$$ 119 : 34 = 3 \text{ ( remainder is } \color{blue}{ 17 } \text{ ) } $$

The remainder is still positive ($ 17 > 0 $), so we will continue with division.

Step 3 :
Divide $ 34 $ by $ \color{blue}{ 17 } $ and get the remainder

$$ 34 : \color{blue}{ \boxed { 17 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 17 }} $.

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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