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

Home > Numbers
N-Divisibility (Posted on 2004-02-29) Difficulty: 3 of 5
How many positive integers divide at least one of 10^40 and 20^30?

  Submitted by DJ    
Rating: 4.1111 (9 votes)
Solution: (Hide)
2301

Factors of 1040 have the form 2m5n with 0 <= m, n <= 40. So there are 41² = 1681 such factors.

Factors of 2030 = 260530 not dividing 1040 have the form 2m5n with 41 <= m <= 60 and 0 <= n <= 30, so there are 20×31 = 620 such factors.

Altogether, there are 1681 + 620 = 2301 numbers matching the problem.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionPuzzle Solution With ExplanationK Sengupta2007-05-28 11:55:32
SolutionsolutionTristan2004-02-29 12:18:43
SolutionsolutionCharlie2004-02-29 11:24:09
SolutionJUST CONT'EMAdy TZIDON2004-02-29 10:37:35
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 (4)
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