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景得 asked in 科學數學 · 7 years ago

資優數學問題正確解答

1到50的整數連乘起來,其結果共有多少個?

(1x2x3x4x5x.........x47x48x49x50)

答案為12個0

但是我用excel product函數驗算卻是得到下列答案

30414093201713400000000000000000000000000000000000000000000000000

這兩者差異究竟為何?

3 Answers

Rating
  • 7 years ago
    Favorite Answer

    1到50的連乘有幾個零, 就是問你這一串數字內有幾個2的倍數與5的倍數, 因為一個2的倍數乘上一個5的倍數就會出現一個0

    2的倍數一定比5的倍數多, 所以算五的倍數就可以了

    1-50, 每五個就有一個5的倍數....5 10 15 20 .... 45 50

    所以可以產生 10 個零.....還沒完

    1-50, 每25個也會再產生一個五的倍數, 25, 50

    所以再產生2個零

    5x5x5 = 125, 已經超出 50 的範圍, 所以不會再有零了

    10+2 = 12

    總共12個零.....

    既然是資優數學, 就應該用推理的, 怎麼會真的去用 EXCEL 算呢....昏倒....

    2014-02-17 12:23:21 補充:

    補充一下, 1x2x3x...x50 就是 50!

    正確答案應該是

    30414093201713378043612608166064768844377641568960512000000000000

    已經超出電腦正常計算的範圍

    Excel 給你的答案是有誤差的

    3.0414093e+64

    所以才會不是 12 個零

  • Anonymous
    7 years ago

    到下面的網址看看吧

    ▶▶http://misshare168.pixnet.net/blog/post/86950298

  • 阿番
    Lv 7
    7 years ago

    50階乘

    =

    30414093201713378043612608166064768844377641568960512000000000000

    1-50 共有10個5的倍數,所以有10個0,又有2個是25的倍數(5*5) ,所以又有2個0,所以總共12個0

    [50/5]+[10/5]=12(個)

    2014-02-17 12:15:04 補充:

    10=2*5

    因組成10有2和5的因數

    若數2的倍數太多,只有數5的倍數較快.

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