To whom it may concern,

I have difficulty in getting the solution to the following question:

Find 5 numbers that have exactly 5 factors.

I got 16, 81 but couldn't find the rest. I believe that in order to have 5 factors, it has to be a square number. Isn't it true? I guess there may be a pattern to this.

Thanks for your help.
Derek

Hi Derek
16 and 81 are squares, but they are also fourth powers. and . Notice also that 2 and 3 are primes.

If p is a prime does have 5 factors?

Since p is a prime, if b divides then b must be a power of p also, with its exponent at most 4. Thus and a is 0, 1, 2, 3 or 4. Hence has 5 factors.

Are primes to the fourth power the only numbers with exactly 5 factors?

Cheers,
Penny