# prime factorization and factors

• Apr 1st 2010, 07:48 PM
ihavvaquestion
prime 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, 07:57 PM
chiph588@
Quote:

Originally Posted by ihavvaquestion
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?

Explain why you think 120 is the correct answer.
• Apr 1st 2010, 08:15 PM
ihavvaquestion
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?