AMC 8 2005 Problem 18
AMC8 2005 年第 18 题
整除与因数★★★☆☆
How many three-digit numbers are divisible by 13?
能被 13 整除的三位数有多少个?
- A.7
- B.67
- C.69
- D.76
- E.77
正确答案 · Correct Answer
C
解析 · Solution
Solution 1
The smallest three-digit number divisible by 13 13 is 13 × 8 = 104 13×8=104, so there are seven two-digit multiples of 13 13. The greatest three-digit number divisible by 13 13 is 13 × 76 = 988 13×76=988. Therefore, there are 76 − 7 = 69 76−7=69 three-digit numbers divisible by 13 13. OR OR Because the integer part of 999 13 13 999 is 76 76, there are 76 76 multiples of 13 13 less than or equal to 999 999. Because the integer part of 99 13 13 99 is 7 7, there are 7 7 multiples of 13 13 less than or equal to 99 99. That means there are 76 − 7 = 69 76−7=69 multiples of 13 13 between 100 100 and 999 999. Answer: 𝐶 C .
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