Step 1 :
Divide $ 14973 $ by $ 4746 $ and get the remainder

$$ 14973 : 4746 = 3 \text{ ( remainder is } \color{blue}{ 735 } \text{ ) } $$

The remainder is positive ($ 735 > 0 $), so we will continue with division.

Step 2 :
Divide $ 4746 $ by $ \color{blue}{ 735 } $ and get the remainder

$$ 4746 : 735 = 6 \text{ ( remainder is } \color{blue}{ 336 } \text{ ) } $$

The remainder is still positive ($ 336 > 0 $), so we will continue with division.

Step 3 :
Divide $ 735 $ by $ \color{blue}{ 336 } $ and get the remainder

$$ 735 : 336 = 2 \text{ ( remainder is } \color{blue}{ 63 } \text{ ) } $$

The remainder is still positive ($ 63 > 0 $), so we will continue with division.

Step 4 :
Divide $ 336 $ by $ \color{blue}{ 63 } $ and get the remainder

$$ 336 : 63 = 5 \text{ ( remainder is } \color{blue}{ 21 } \text{ ) } $$

The remainder is still positive ($ 21 > 0 $), so we will continue with division.

Step 5 :
Divide $ 63 $ by $ \color{blue}{ 21 } $ and get the remainder

$$ 63 : \color{blue}{ \boxed { 21 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 21 }} $.

This solution can be visualized using a Venn diagram.

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

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