SOLUTION: The product of 3 different prime numbers is always divisible by exactly _____ (how many) different non-prime numbers greater than 1?

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Question 1139003: The product of 3 different prime numbers is always divisible by exactly _____ (how many) different non-prime numbers greater than 1?

Answer by ikleyn(52914) About Me  (Show Source):
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If  N = p*q*r  is the product of 3 prime numbers p, q and r, then

 
the divisors of N, that are not 1 or primes are  pq, pr, qr and the number N itself.


So, the answer is 4, equal to the cardinality of the set  {pq, pr, qr, N }.


ANSWER.  4.