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A stupid math question

What is the smallest integer greater than 0 that can be written entirely with zeros and ones and is evenly divisible by 225?

I need the process(steps)

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  • 1 decade ago
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    What is the smallest integer greater than 0 that can be written entirely with zeros and ones and is evenly divisible by 225?

    能被225整除的最小整數,且數字只能是0和1……

    225 = 9*5*5.

    能夠被225整除,一定能被9整除。能夠被9整除,其各個位數數字和必須為9(例如:9, 18, 27, 36, 45, 54, 63, 72, 81, 90, etc.),因此最小的數必定包含9個1:111 111 111。

    能夠被225整除,一定能被25整除。能夠被25整除,且不包含"5"這個數字,則必定是100的倍數(25, 50, 75, 125, 150, 175, 225等都不符合條件)。

    因此,綜合上面兩個條件,能被225整除的最小整數,且數字只包含0和1的最小整數是:11,111,111,100。

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  • Frank
    Lv 7
    1 decade ago

    看了我頭都昏了.....

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  • 1 decade ago

    That"s my stupid answer for the stupid math question.

    What is the smallest integer greater than 0 that can be written entirely with zeros and ones and is evenly divisible by 225?

    譯題:

    找出一個大於零的最小整數(N)

    該數字A:全用1或0寫成

    又能B:被225整除.

    所以N=(9*2)*(25*4)*X=1800*X

    X最小為1....即N=1800時

    符合條件A及B

    1.8.0等3個數字都符合條件A

    (8是由兩個0寫成)

    225=9*25

    要符合條件A時,

    該數字必為9的偶數倍數為18(9*2)或81(9*9)

    且為25的4倍數(25*4=100)

    所以N=(9*2)*(25*4)*X=1800*X

    X最小為1....即N=1800時

    符合條件A及B

    2008-04-23 09:59:01 補充:

    如果把9也看成由1和0組成的數字

    則N=(9*1)*(25*4)*X=900*X

    最小為900!!

    2008-04-23 10:02:46 補充:

    說明一下:

    "該數字必為9的偶數倍數為18(9*2)或81(9*9)"

    但18<81

    所以選擇18

    2008-04-23 10:12:08 補充:

    jyeh30是正統數學思路

    媗媽的答案是腦筋急轉彎囉!!

    (The stupid math question~~)

    2008-04-23 11:41:04 補充:

    to熾焰:

    哈!!大師客氣了~~

    昏頭聽聽西洋音樂放鬆一下囉~~

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