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Posted by on Thursday, January 10, 2013 at 9:37pm.

For how many positive integers n does n! end in exactly 5 0s?

  • math - , Thursday, January 10, 2013 at 10:26pm

    we get a zero when we multiply be a number ending in either 2 and 5 or a 10
    at the end of 5! --- one zero
    at the end of 10! -- two zeros
    at the end of 15! -- 3 zeros
    at the end of 20! -- 4 zeros
    at the end of 25! -- 5 zeros

    e.g.
    10! = 10x9x8x7x6x5x5x3x2x1
    = 2x5x3x3x2x2x2x7x3x2x5x2x2x3x2
    = (2^8 x 5^2) x 3^4 x 7
    = 6400 x 567 --- ending in 2 zeros

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