AMC 8 1997 Problem 11

AMC8 1997 年第 11 题

整除与因数★★★☆☆

Let

\boxed{N}

mean the number of whole number divisors of

N

. For example,

\boxed{3}=2

because 3 has two divisors, 1 and 3. Find the value of

\boxed{\boxed{11}\times\boxed{20}}.

令

\boxed{N}

表示

N

的正整数因数的个数。例如

\boxed{3}=2

，因为 3 有两个因数：1 和 3。求

\boxed{\boxed{11}\times\boxed{20}}

的值。

正确答案 · Correct Answer

解析 · Solution

Solution 1

11×2011 has 2 factors, and 20 has

\{1, 2, 4, 5, 10, 20\}

as factors, for a total of 6 factors. Plugging 11 = 2 and 20= 6:

2×61212 has factors of

\{1, 2, 3, 4, 6, 12\}

, so 12 = 6, and the answer is

A

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