Suppose n is a natural number that satisfies the following conditions, they are multiples of 75 and have exactly 75 natural number factors (including 1 and itself), find the minimum value of ((n)/75).
设n是满足下列条件的自然数，它们是75的倍数且恰好有75个自然数因数(包括1和本身)，求((n)/75)的最小值．
<gadget id="calculator">5 ** 2</gadget>
<output>25</output>

<gadget id="calculator">3 ** 4</gadget>
<output>81</output>

<gadget id="calculator">2 ** 4</gadget>
<output>16</output>

<gadget id="calculator">25 * 81 * 16</gadget>
<output>32_400</output>

<gadget id="calculator">32_400 / 75</gadget>
<output>432</output>

<result>432</result>