What number has exactly 6 proper factors?

Answer 1

16 can be factored in several ways, for example:

1) 16

2) 4 x 4

3) 8 x 2

4) 4 x 2 x 2

Here are products of prime numbers that correspond to each of these cases. Note that the exponent is always one less than the factor in the above list.

1) 215, 315, 515, etc.

2) 23 x 33 (or any other prime numbers raised to the same powers)

3) 57 x 111

4) 23 x 31 x 51

In any of these cases, and other factorizations, each factor (the base) can be replaced by any Prime number.

Answer 2

Assuming you mean 20 different factors, 1x2x3x5x7x11x13x17x19x23x29x31x37x41x43x47x53x59x61x67

Use a calculator to get the answer.

Notice that all I've done is list the first 20 prime numbers.

Otherwise if factors are allowed to repeat, the answer is 1. 1x1x1x... (list it 20times) and the answer is 1

This is usually referred to as a trivial answer.

Answer 3

24 does.