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HMMT 二月 2009 · 冲刺赛 · 第 7 题

HMMT February 2009 — Guts Round — Problem 7

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 6 ] How many perfect squares divide 2 · 3 · 5 · 7 ?
解析

英文解析

  1. [ 6 ] How many perfect squares divide 2 · 3 · 5 · 7 ?
    Answer: 120
    Solution: The number of such perfect squares is 2 · 3 · 4 · 5, since the exponent of each prime can beany nonnegative even number less than the given exponent.