All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
The final quantity (Posted on 2015-02-18) Difficulty: 2 of 5
Given a list of all composite numbers below 1000, how many will remain after erasure of numbers divisible by 2,3 or 5?

Rem1: "or" is inclusive i.e. and/or.
Rem2: number 1 is neither prime nor composite, so it does not appear on the initial list.

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
A third method by hand Comment 4 of 4 |
The LCM (Least Common Multiple) or 2,3, and 5 is 30.  There are 8 numbers between 1 and 30 that are not divisible by 2, 3 or 5.  There are 2 numbers between 1 and 9 that are not divisible by 2, 3 or 5.

999 = 33*30 + 9, so there are 33*8 + 2 = 266 numbers less than 1000 that are not divisible by 2, 3 or 5.

But these include primes.  There are 168 primes under 1000, but these include 2,3,and 5.  There are therefore 165 primes under 1000 that are not divisible by 2,3,and 5.

266 - 165 = 101, so there are 101 non-primes under 1000 that are not divisible by 2,3, or 5.  One of these (1) is neither prime nor composite, and needs to be subtracted out also.

Final answer = 100.

  Posted by Steve Herman on 2015-02-19 22:15:37
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information