1个数除5余3,除6余4,除7余1,这样的3位数有几个?

作者: tihaiku 人气: - 评论: 0
问题 1个数除5余3,除6余4,除7余1,这样的3位数有几个?
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答案 5
解析 解析:这个数加2后同时能被 5和6整除,所以加 2后能被30整除,且除以7余3,被30整除的最小三位数是 120,不满足除以7余3,而150满足除以7余3,若比150大的数除以7也余3,则要在50的基础上增加7的倍数,而每次增加又要是30的倍数,所以每次应该加210,所以满足要求的三位数是:150-2=148,150+210-2=360-2=358,150+420-2=568,150+630=778,150+840-2=988,一共有 5个.

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