Step 1 :
Divide $ 2352 $ by $ 1442 $ and get the remainder

$$ 2352 : 1442 = 1 \text{ ( remainder is } \color{blue}{ 910 } \text{ ) } $$

The remainder is positive ($ 910 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1442 $ by $ \color{blue}{ 910 } $ and get the remainder

$$ 1442 : 910 = 1 \text{ ( remainder is } \color{blue}{ 532 } \text{ ) } $$

The remainder is still positive ($ 532 > 0 $), so we will continue with division.

Step 3 :
Divide $ 910 $ by $ \color{blue}{ 532 } $ and get the remainder

$$ 910 : 532 = 1 \text{ ( remainder is } \color{blue}{ 378 } \text{ ) } $$

The remainder is still positive ($ 378 > 0 $), so we will continue with division.

Step 4 :
Divide $ 532 $ by $ \color{blue}{ 378 } $ and get the remainder

$$ 532 : 378 = 1 \text{ ( remainder is } \color{blue}{ 154 } \text{ ) } $$

The remainder is still positive ($ 154 > 0 $), so we will continue with division.

Step 5 :
Divide $ 378 $ by $ \color{blue}{ 154 } $ and get the remainder

$$ 378 : 154 = 2 \text{ ( remainder is } \color{blue}{ 70 } \text{ ) } $$

The remainder is still positive ($ 70 > 0 $), so we will continue with division.

Step 6 :
Divide $ 154 $ by $ \color{blue}{ 70 } $ and get the remainder

$$ 154 : 70 = 2 \text{ ( remainder is } \color{blue}{ 14 } \text{ ) } $$

The remainder is still positive ($ 14 > 0 $), so we will continue with division.

Step 7 :
Divide $ 70 $ by $ \color{blue}{ 14 } $ and get the remainder

$$ 70 : \color{blue}{ \boxed { 14 }} = 5 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 14 }} $.

This solution can be visualized using a Venn diagram.

The GCD equals the product of the numbers at the intersection.

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