Find all natural numbers n such that when we multiply all divisors of n, we will obtain 10^{9}. Prove that your number(s) n works and that there are no other such numbers.
(Note: A natural number n is a positive integer; i.e., n is among the counting numbers 1,2,3, \ldots A divisor of n is a natural number that divides n without any remainder. For example, 5 is a divisor of 30 because 30 \div 5=6; but 5 is not a divisor of 47 because 47 \div 5=9 with remainder 2. In this problem we consider only positive integer numbers n and positive integer divisors of n. Thus, for example, if we multiply all divisors of 6 we will obtain 36.)