Step 1 :
Divide $ 12435648 $ by $ 37451 $ and get the remainder

$$ 12435648 : 37451 = 332 \text{ ( remainder is } \color{blue}{ 1916 } \text{ ) } $$

The remainder is positive ($ 1916 > 0 $), so we will continue with division.

Step 2 :
Divide $ 37451 $ by $ \color{blue}{ 1916 } $ and get the remainder

$$ 37451 : 1916 = 19 \text{ ( remainder is } \color{blue}{ 1047 } \text{ ) } $$

The remainder is still positive ($ 1047 > 0 $), so we will continue with division.

Step 3 :
Divide $ 1916 $ by $ \color{blue}{ 1047 } $ and get the remainder

$$ 1916 : 1047 = 1 \text{ ( remainder is } \color{blue}{ 869 } \text{ ) } $$

The remainder is still positive ($ 869 > 0 $), so we will continue with division.

Step 4 :
Divide $ 1047 $ by $ \color{blue}{ 869 } $ and get the remainder

$$ 1047 : 869 = 1 \text{ ( remainder is } \color{blue}{ 178 } \text{ ) } $$

The remainder is still positive ($ 178 > 0 $), so we will continue with division.

Step 5 :
Divide $ 869 $ by $ \color{blue}{ 178 } $ and get the remainder

$$ 869 : 178 = 4 \text{ ( remainder is } \color{blue}{ 157 } \text{ ) } $$

The remainder is still positive ($ 157 > 0 $), so we will continue with division.

Step 6 :
Divide $ 178 $ by $ \color{blue}{ 157 } $ and get the remainder

$$ 178 : 157 = 1 \text{ ( remainder is } \color{blue}{ 21 } \text{ ) } $$

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

Step 7 :
Divide $ 157 $ by $ \color{blue}{ 21 } $ and get the remainder

$$ 157 : 21 = 7 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

The remainder is still positive ($ 10 > 0 $), so we will continue with division.

Step 8 :
Divide $ 21 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 21 : 10 = 2 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

The remainder is still positive ($ 1 > 0 $), so we will continue with division.

Step 9 :
Divide $ 10 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 10 : \color{blue}{ \boxed { 1 }} = 10 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.

This solution can be visualized using a Venn diagram.

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

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