How many positive integer factors of 100 factorial, are multiples of 2 or 3?

Question

Mathematics

Keaton Alvarado

14 May, 19:14

How many positive integer factors of 100 factorial, are multiples of 2 or 3?

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Answers (1)

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Orlando Chambers · Answer 1

100 factorial is 1*2*3 * ... * 100

Number of multiples of 2 less than 100 = 49

Number of multiples of 3 less than 100 = 33

We are double counting those that are multiples of 2 and 3 (or 6)

Number of multiples of 6 less than 100 = 16

49+33-16 = 66

There are 66 factors that are multiples or 2 or 3