AMC10 2014 B

AMC10 2014 B · Q12

AMC10 2014 B · Q12. It mainly tests Primes & prime factorization, Counting divisors.

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

2,014,000,000 的最大除数是它本身。它的第五大除数是多少？

(A) 125,875,000 125,875,000

(B) 201,400,000 201,400,000

(D) 402,800,000 402,800,000

(E) 503,500,000 503,500,000

Answer

Correct choice: (C)

正确答案：（C）

Solution

By inspection, the five smallest positive divisors of 2,014,000,000 are 1, 2, 4, 5, and 8. Therefore the fifth largest divisor is $\frac{2,014,000,000}{8} = 251,750,000$.

通过检查，2,014,000,000 的五个最小正除数是 1、2、4、5 和 8。因此第五大除数是 \frac{2,014,000,000}{8} = 251,750,000。

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