Find n where 2ⁿ is the largest power of 2 that divides the product 2011*2012*2013*.....*4022

Ans: 2005

1001+501+250+    9+5+1+1=2005

1001 numbers divisible by 2^1

501 umbers divisible by 2^2

250  divisible by 2^3

.....etc....

9       divisible by 2^8

5       divisible by 2^9

1 number divisible by 2^10

and one      number  by 2^11:

total 2005

 

Edited on December 5, 2011, 12:54 pm

Posted by Ady TZIDON on 2011-12-05 12:51:57