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HMMT 二月 2007 · 冲刺赛 · 第 5 题

HMMT February 2007 — Guts Round — Problem 5

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 6 ] Compute the largest positive integer such that is an integer. n 2007
解析
  1. [ 6 ] Compute the largest positive integer such that is an integer. n 2007 2 Answer: 9 . Note that 2007 = 3 · 223. Using the fact that the number of times a prime p divides n ! is given by ⌊ ⌋ ⌊ ⌋ ⌊ ⌋ n n n
      • · · · , 2 3 p p p it follows that the answer is 9.