Find maximum power of 3 in 24!

radha gogia

radha gogia

@radha-BTDzli • Oct 22, 2024
upload_2014-10-20_10-42-41

Please tell the approach of solving ques 25.
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  • Kaustubh Katdare

    Kaustubh Katdare

    @thebigk • Oct 19, 2014

    I'm typing it for the benefit of the community here 😀

    It is desired to extract maximum power of 3 from 24! where n! = n.(n-1).(n-2)...3.2.1. What will be exponent of 3?

    Options:
    a) 8 b) 9 c) 11 d)10

    Since this is a math question, I'm moving this to proper section. Also updated the title to make it obvious to know what's the question about.
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  • Ramani Aswath

    Ramani Aswath

    @ramani-VR4O43 • Oct 19, 2014

    The factors must be themselves multiples of 3. In this case these are: 3, 6, 9, 12, 15, 18, 21 & 24.
    the powers of 3 in these are, 1, 1, 2, 1, 1, 2, 1 &1 respectively.
    The highest power of three that can be got by a product of these 8 factors is the sum of the 8 powers = 10.
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  • satyam Dubey

    satyam Dubey

    @satyam-P9vodx • Sep 12, 2018

    50! Maximum power 5


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