There are an infinite number of them. 8 has three prime factors, 30 is the first with three distinct prime factors.
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A prime number is a positive integer that has exactly two different factors: 1 and itself. This is why 1 is not a prime number: it has the factors 1 and itself, but they are the same - it does not have exactly two different factors.
Prime numbers.
Take any 5 prime numbers and multiply them together.
Prime numbers have exactly two factors. 53 and 59 are prime numbers.
Any number of the form a*b^4 where a and b are different prime numbers, or c^9 where c is a prime, will have exactly 10 factors.