Find Greatest Common Divisor of 14039 and 1529, using Euclidean algorithm.

Answer

The GCD of given numbers is 139.

Step 1 :
Divide $ 14039 $ by $ 1529 $ and get the remainder

$$ 14039 : 1529 = 9 \text{ ( remainder is } \color{blue}{ 278 } \text{ ) } $$

The remainder is positive ($ 278 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1529 $ by $ \color{blue}{ 278 } $ and get the remainder

$$ 1529 : 278 = 5 \text{ ( remainder is } \color{blue}{ 139 } \text{ ) } $$

The remainder is still positive ($ 139 > 0 $), so we will continue with division.

Step 3 :
Divide $ 278 $ by $ \color{blue}{ 139 } $ and get the remainder

$$ 278 : \color{blue}{ \boxed { 139 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 139 }} $.

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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