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  What is the least positive integer that is not a factor of 25! and is not a prime number?

  A. 26

  B. 28

  C. 36

  D. 56

  E. 58

  解答:25!指的是 25 阶乘=25*24*...*1

  5 显然是 factor

  6,7,8,9,10,...,25 显然都是 factor

  26=2*13 也是

  27=3*3*3, 25!中有 3 和 9,所以也是 factor

  28=4*7,factor

  29 是 prime

  30=3*10

  31prime

  32=4*8,factor

  33=3*11,factor

  34=2*17,factor

  35=5*7,factor

  36=4*9,factor

  37prime

  38=2*19,factor

  39prime

  40=4*10,factor

  41prime

  42=2*21factor

  43prime

  44=4*11factor

  45=5*9factor

  46=2*23factor

  47prime

  48=6*8factor

  49=7*7,25!包含 7 和 14, factor

  50=5*10factor

  51=3*17factor

  52=4*13factor

  53prime

  54=2*3*9,factor

  55=5*11,factor

  56=7*8,factor

  57=3*19,factor

  58=2*29,not a factor and not a prime

  所以 58 is the least positive integer that is not a factor of 25! and is not a prime number.

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