Let's calculate: <math><mi>pgcd</mi><mo>(</mo><mn>24</mn><mo>, </mo><mn>36</mn><mo>)</mo></math>
Let's decompose: <math><mn>24</mn></math> into prime factors:
 <math><mn>2</mn><mo>×</mo><mn>12</mn></math>
 <math><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>×</mo><mn>6</mn></math>
 <math><msup><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></msup><mo>×</mo><mn>3</mn></math>
Let's decompose: <math><mn>36</mn></math> into prime factors:
 <math><mn>2</mn><mo>×</mo><mn>18</mn></math>
 <math><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>×</mo><mn>9</mn></math>
 <math><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>×</mo><mn>3</mn><mo>×</mo><mn>3</mn></math>
 <math><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>×</mo><msup><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></msup></math>
To obtain the GCD, we keep the common prime factors with the smallest exponent: 2^2*3
 <math><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>×</mo><mn>3</mn></math>
 <math><mn>4</mn><mo>×</mo><mn>3</mn></math>

▷<b>Answer: &nbsp; <math><mn>12</mn></math></b><span style='font-size:smaller'> &nbsp; &nbsp; (computation required 13 steps and 0 ms)</span>