How many n in a factorial?

GRE Quant Problem Solving
1

I am unable to understand this flash card from group 2 quant. is anyone there to explain this? Thank you!

2

See the “# of Numbers in Factorials” video on PrepSwift.

3

Bumping this question - I don’t understand the flashcard and I am not following prepswift / have an account with them. I am following Greg’s videos.

4

Explain the issue you’re having with the concept, in detail.

5

Hi, I am also having some difficulty understanding how this trick works.

On the flashcard, how many multiples from 1 to 30, I got 3,6,9,12,15 etc. But I see 3, 3 to the power of 2 and 3 to the power of 3 are listed. How did you get to this step? Also, how did you get the numbers underneath? 10+3+1=14

Thank you very much for your time! I have access to study plans but not prepswift.

6

Notice that 9 has 2 3s. So

  • you indeed get 10 3s from 3, 6, 9, …, 30.
  • But the numbers 9, 18 and 27 have another 3 we need to consider.
  • And can you show that the number 27 has another 3?
7

Thank you!
Is it because 27=3 cubed? We counted 3 once to get 10, then second round of 3 by counting 3 squared to get 3, and lastly 27 has one more 3 for a total of 10+3+1=14

8

Indeed.