Divisibility 2015

Number Theory Level 3

Find the number of elements in the set, {1!,2!,3!,........,5102!} which are divisible by 2015.

5174 2015 5172 5072 5074 5102

Nelson Mandela by Nelson Mandela , 21, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

since 2015 has prime factors of 5 13 31, then elements more than or equal to 31! in the set will be divisible by 2015, since 31! and above will all contain the prime factors of 2015. Thus, the number of elements divisible by 2015 in the set will be 5102-31+1 (as 31! is included)

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Correct! upvoted. Try the whole set and try to post a solution for each question. Keep it up. https://brilliant.org/profile/nelson-akpier/sets/functions/

Nelson Mandela - 5 years, 11 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...