AMC8 2005

AMC8 2005 · Q18

AMC8 2005 · Q18. It mainly tests Arithmetic misc, Divisibility & factors.

How many three-digit numbers are divisible by 13?

多少个三位数能被13整除？

(A) 7 7

(B) 67 67

(D) 76 76

(E) 77 77

Answer

Correct choice: (C)

正确答案：（C）

Solution

(C) The smallest three-digit number divisible by 13 is $13\times 8=104$, so there are seven two-digit multiples of 13. The greatest three-digit number divisible by 13 is $13\times 76=988$. Therefore, there are $76-7=69$ three-digit numbers divisible by 13.

（C）能被13整除的最小三位数是 $13\times 8=104$，因此有7个两位数的13的倍数。能被13整除的最大三位数是 $13\times 76=988$。所以，能被13整除的三位数共有 $76-7=69$ 个。

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