Question

数 $2,014,000,000$ 的最大因数是它本身。它的第五大因数是多少？

The largest divisor of $2,014,000,000$ is itself. What is its fifth-largest divisor?

$125, 875, 000$

$201, 400, 000$

$251, 750, 000$

$402, 800, 000$

$503, 500, 000$

答案：C

知识点：因数质因数分解

难度评级：1280

解答：

第五大因数等于 $2,014,000,000$ 除以第五小因数。

$2,014,000,000$ 的素因数分解为最小的 $5$ 个因数是 $1,2,4,5,8$ 。所以第五小因数为 $8$ ，第五大因数为 $2^7\cdot 5^6 \cdot 19\cdot 53.$ $\dfrac{2014000000}8 =251750000.$

所以正确答案是 C。

The fifth-largest divisor is $2,014,000,000$ divided by the fifth smallest divisor.

The prime factorization of $2,014,000,000$ is: $2^7\cdot 5^6 \cdot 19\cdot 53.$ This makes the first $5$ smallest divisors $1,2,4,5,8$ Therefore, the fifth smallest divisor is $8,$ and the fifth largest divisor must be: $\dfrac{2014000000}8 =251750000.$

Thus, the correct answer is C .

2014 AMC 10B 第 12 题

答案：C

难度评级：1280

解答：

其他年份的第 12 题