Question

$2010$ 的质因数之和是多少？

What is the sum of the prime factors of $2010?$

$\ 67$

$\ 75$

$\ 77$

$\ 201$

$\ 210$

答案：C

知识点：质因数分解

难度评级：960

解答：

首先，质数 $2,5$ 是 $2010$ 的因数，因为它是 $10$ 的倍数。 $2010$ 除以 $10$ 得 $201$ 。接着， $3$ 是 $201$ 的因数，因为 $201$ 的数位和是 $3$ 的倍数。再除以 $3$ 得到质数 $67$ 。因此质因数为 $2,3,5,67$ ，它们的和为 $77$ 。

所以正确答案是 C。

First, the primes $2,5$ are factors of $2010$ since it is a multiple of $10.$ Dividing $2010$ by $10$ is $201.$ Then, $3$ is a factor of $201$ since the digit sum of $201$ is a multiple of $3.$ Dividing this by $3$ yields the prime number $67.$ This means the prime factors are $2,3,5,67,$ which makes their sum $77.$

Thus, the correct answer is C .

2010 AMC 8 第 14 题

答案：C

难度评级：960

解答：

其他年份的第 14 题