Wednesday, July 1, 2009

Problem of the day 1.07.09

300! is divisible by (24!)^n. what is the max. possible integral value of n?
Posted by Unknown at 2:35 PM
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11 comments:

  1. anupJuly 1, 2009 at 7:44 PM

    max. possible integral value of n is...3

    ReplyDelete
  2. NareshJuly 1, 2009 at 9:29 PM

    MAximum value of n is 12

    ReplyDelete
  3. RahulJuly 1, 2009 at 9:45 PM

    Both of you have got it wrong

    ReplyDelete
  4. anupJuly 2, 2009 at 11:54 AM

    den is it 13???..plz send me d soln..

    ReplyDelete
  5. RahulJuly 2, 2009 at 11:57 AM

    The highest prime in 24! is 23

    so the n will be limited by the power of 23 in 300!

    Now solve!

    ReplyDelete
  6. yodhaJuly 3, 2009 at 2:44 PM

    yes the power of the highest prime will determine the value of 23.
    hence the answer is 13 + 1 =14.

    ReplyDelete
  7. RahulJuly 3, 2009 at 2:46 PM

    Answer is 13 yodha! why do u add 1?

    ReplyDelete
  8. yodhaJuly 4, 2009 at 7:50 PM

    sorry just made a slight error.
    i added 1 with the thought 300/13^2 (i.e. considered the power of 13). now u can understand. how big is this error.

    sorry for that.

    ReplyDelete
  9. saurabhJuly 28, 2009 at 4:34 PM

    hi rahul..it may b too trivial to ask but can u explain as in y the highest power of prime would be the determining factor,also y cant the power of 24 do?

    ReplyDelete
  10. RahulJuly 28, 2009 at 5:42 PM

    because 24=2^3x3

    there will be many 2s and 3s in 300!
    but there will be very few 23s.

    I hope u get it!

    ReplyDelete
  11. saurabhJuly 28, 2009 at 10:34 PM

    thnx a lot

    ReplyDelete

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