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Problem of the day 1.07.09

with 11 comments


300! is divisible by (24!)^n. what is the max. possible integral value of n?

Written by Implex

July 1, 2009 at 9:05 am

11 Responses

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

    anup

    July 1, 2009 at 2:14 pm

  2. MAximum value of n is 12

    Naresh

    July 1, 2009 at 3:59 pm

    • Both of you have got it wrong

      Rahul

      July 1, 2009 at 4:15 pm

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

        anup

        July 2, 2009 at 6:24 am

  3. The highest prime in 24! is 23

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

    Now solve!

    Rahul

    July 2, 2009 at 6:27 am

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

    yodha

    July 3, 2009 at 9:14 am

  5. Answer is 13 yodha! why do u add 1?

    Rahul

    July 3, 2009 at 9:16 am

  6. 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.

    yodha

    July 4, 2009 at 2:20 pm

  7. 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?

    saurabh

    July 28, 2009 at 11:04 am

  8. because 24=2^3×3

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

    I hope u get it!

    Rahul

    July 28, 2009 at 12:12 pm


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