Step 1 :
Divide $ 17570 $ by $ 12750 $ and get the remainder

$$ 17570 : 12750 = 1 \text{ ( remainder is } \color{blue}{ 4820 } \text{ ) } $$

The remainder is positive ($ 4820 > 0 $), so we will continue with division.

Step 2 :
Divide $ 12750 $ by $ \color{blue}{ 4820 } $ and get the remainder

$$ 12750 : 4820 = 2 \text{ ( remainder is } \color{blue}{ 3110 } \text{ ) } $$

The remainder is still positive ($ 3110 > 0 $), so we will continue with division.

Step 3 :
Divide $ 4820 $ by $ \color{blue}{ 3110 } $ and get the remainder

$$ 4820 : 3110 = 1 \text{ ( remainder is } \color{blue}{ 1710 } \text{ ) } $$

The remainder is still positive ($ 1710 > 0 $), so we will continue with division.

Step 4 :
Divide $ 3110 $ by $ \color{blue}{ 1710 } $ and get the remainder

$$ 3110 : 1710 = 1 \text{ ( remainder is } \color{blue}{ 1400 } \text{ ) } $$

The remainder is still positive ($ 1400 > 0 $), so we will continue with division.

Step 5 :
Divide $ 1710 $ by $ \color{blue}{ 1400 } $ and get the remainder

$$ 1710 : 1400 = 1 \text{ ( remainder is } \color{blue}{ 310 } \text{ ) } $$

The remainder is still positive ($ 310 > 0 $), so we will continue with division.

Step 6 :
Divide $ 1400 $ by $ \color{blue}{ 310 } $ and get the remainder

$$ 1400 : 310 = 4 \text{ ( remainder is } \color{blue}{ 160 } \text{ ) } $$

The remainder is still positive ($ 160 > 0 $), so we will continue with division.

Step 7 :
Divide $ 310 $ by $ \color{blue}{ 160 } $ and get the remainder

$$ 310 : 160 = 1 \text{ ( remainder is } \color{blue}{ 150 } \text{ ) } $$

The remainder is still positive ($ 150 > 0 $), so we will continue with division.

Step 8 :
Divide $ 160 $ by $ \color{blue}{ 150 } $ and get the remainder

$$ 160 : 150 = 1 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 9 :
Divide $ 150 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 150 : \color{blue}{ \boxed { 10 }} = 15 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 10 }} $.

This solution can be visualized using a Venn diagram.

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

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