What is the smallest whole number that has exactly 16 factors?

i think i understand this type of problem, but i am looking for confirmation...is 120 the correct answer?

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- Apr 1st 2010, 06:48 PMihavvaquestionprime factorization and factors
What is the smallest whole number that has exactly 16 factors?

i think i understand this type of problem, but i am looking for confirmation...is 120 the correct answer? - Apr 1st 2010, 06:57 PMchiph588@
- Apr 1st 2010, 07:15 PMihavvaquestion
chip i think its because in terms of prime factorization a number that has exactly 16 factors has to look like one of the following:

16*1 = p^15

4*4 = p^3*q^3

2*2*2*2 = pqrs

4*2*2 = p^3*qr

8*2= p^7*q

looking at these i checked them out and using the smallest primes i figured the first and last ones to be way too big, but

2^3*3^3 = 216

2*3*5*7 = 210

2^3*3*5 = 120

so 120 must be the smallest whole number that has exactly 16 factors...right?