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HMMT 十一月 2008 · 冲刺赛 · 第 13 题

HMMT November 2008 — Guts Round — Problem 13

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 9 ] Find the number of distinct primes dividing 1 · 2 · 3 · · · 9 · 10.
解析
  1. [ 9 ] Find the number of distinct primes dividing 1 · 2 · 3 · · · 9 · 10. Answer: 4 A prime divides this product if and only if it divides one of the multiplicands, so prime divisors of this product must be less than 10. There are 4 primes less than 10, namely, 2, 3, 5, and 7.