Find Greatest Common Divisor of 85672 and 242040, using Euclidean algorithm.

Answer

The GCD of given numbers is 8.

Step 1 :
Divide $ 242040 $ by $ 85672 $ and get the remainder

$$ 242040 : 85672 = 2 \text{ ( remainder is } \color{blue}{ 70696 } \text{ ) } $$

The remainder is positive ($ 70696 > 0 $), so we will continue with division.

Step 2 :
Divide $ 85672 $ by $ \color{blue}{ 70696 } $ and get the remainder

$$ 85672 : 70696 = 1 \text{ ( remainder is } \color{blue}{ 14976 } \text{ ) } $$

The remainder is still positive ($ 14976 > 0 $), so we will continue with division.

Step 3 :
Divide $ 70696 $ by $ \color{blue}{ 14976 } $ and get the remainder

$$ 70696 : 14976 = 4 \text{ ( remainder is } \color{blue}{ 10792 } \text{ ) } $$

The remainder is still positive ($ 10792 > 0 $), so we will continue with division.

Step 4 :
Divide $ 14976 $ by $ \color{blue}{ 10792 } $ and get the remainder

$$ 14976 : 10792 = 1 \text{ ( remainder is } \color{blue}{ 4184 } \text{ ) } $$

The remainder is still positive ($ 4184 > 0 $), so we will continue with division.

Step 5 :
Divide $ 10792 $ by $ \color{blue}{ 4184 } $ and get the remainder

$$ 10792 : 4184 = 2 \text{ ( remainder is } \color{blue}{ 2424 } \text{ ) } $$

The remainder is still positive ($ 2424 > 0 $), so we will continue with division.

Step 6 :
Divide $ 4184 $ by $ \color{blue}{ 2424 } $ and get the remainder

$$ 4184 : 2424 = 1 \text{ ( remainder is } \color{blue}{ 1760 } \text{ ) } $$

The remainder is still positive ($ 1760 > 0 $), so we will continue with division.

Step 7 :
Divide $ 2424 $ by $ \color{blue}{ 1760 } $ and get the remainder

$$ 2424 : 1760 = 1 \text{ ( remainder is } \color{blue}{ 664 } \text{ ) } $$

The remainder is still positive ($ 664 > 0 $), so we will continue with division.

Step 8 :
Divide $ 1760 $ by $ \color{blue}{ 664 } $ and get the remainder

$$ 1760 : 664 = 2 \text{ ( remainder is } \color{blue}{ 432 } \text{ ) } $$

The remainder is still positive ($ 432 > 0 $), so we will continue with division.

Step 9 :
Divide $ 664 $ by $ \color{blue}{ 432 } $ and get the remainder

$$ 664 : 432 = 1 \text{ ( remainder is } \color{blue}{ 232 } \text{ ) } $$

The remainder is still positive ($ 232 > 0 $), so we will continue with division.

Step 10 :
Divide $ 432 $ by $ \color{blue}{ 232 } $ and get the remainder

$$ 432 : 232 = 1 \text{ ( remainder is } \color{blue}{ 200 } \text{ ) } $$

The remainder is still positive ($ 200 > 0 $), so we will continue with division.

Step 11 :
Divide $ 232 $ by $ \color{blue}{ 200 } $ and get the remainder

$$ 232 : 200 = 1 \text{ ( remainder is } \color{blue}{ 32 } \text{ ) } $$

The remainder is still positive ($ 32 > 0 $), so we will continue with division.

Step 12 :
Divide $ 200 $ by $ \color{blue}{ 32 } $ and get the remainder

$$ 200 : 32 = 6 \text{ ( remainder is } \color{blue}{ 8 } \text{ ) } $$

The remainder is still positive ($ 8 > 0 $), so we will continue with division.

Step 13 :
Divide $ 32 $ by $ \color{blue}{ 8 } $ and get the remainder

$$ 32 : \color{blue}{ \boxed { 8 }} = 4 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 8 }} $.

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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