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1 trillion as two factors

  1. Dec 31, 2009 #1
    Can anyone tell me how to factor 1 trillion in 2 numbers, and none of them have zeroes in them?

    Thanks.
     
  2. jcsd
  3. Dec 31, 2009 #2
    The two numbers I got were 262,144 x 3,814,697.266 and 5^12 x 2^12. I'm not sure which one is right because the first one I'm not sure if it's exact and the second one technically has zeroes.
     
  4. Dec 31, 2009 #3
    Usually in riddles of this nature the "two numbers" are assumed to be integers.

    Perhaps the riddle meant the British definition of "trillion", 10^18, in which case your factors would be 2^18 and 5^18, (262144 and 3814697265625).
     
  5. Dec 31, 2009 #4
    I'm American, and it's an American school so I'm pretty sure it mean 10^12.

    Thanks though.
     
  6. Dec 31, 2009 #5
    It's straightforward to prove that 5^12 x 2^12 is the only factorization into two factors such that neither of the two ends with zero. (Because any factor that has a 2 and a 5 would be divisible by ten.)
     
  7. Dec 31, 2009 #6
    It's not that it can't end in zero, it just can't have any zeros in it.
     
  8. Dec 31, 2009 #7
    Then some trick must be involved. Either you're allowed to use non-integer factors, or you're allowed to use non-decimal systems.
     
  9. Jan 1, 2010 #8

    HallsofIvy

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    [itex]2^12= 4096[/itex] and [itex]5^12= 244140625[/itex], both of which have 0s so [math](2^12)(5^12([/math] and with any other two factors at least one would have to have factors of "2" and "5" and so be a multiple of 10.
     
  10. Jan 1, 2010 #9

    Borek

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    1*1717914916

    Edit: on the second reading I see hamster already hinted at this solution.
     
  11. Jan 1, 2010 #10
    Isn't this sum wrong anyway, as 1 trillion (either long or short scale), 10 and 16 are all co-prime to 2, so it cannot end in an odd "digit"? ;)
     
  12. Jan 1, 2010 #11

    Borek

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    No idea what have happened, obviously some finger slip on my side. 1*34771513724319 looks much better.
     
  13. Jan 1, 2010 #12

    Astronuc

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    262,144 x 3814697.265625 works if one is allowed decimals.
     
  14. Jan 1, 2010 #13
    We are allowed decimals. Thanks for the answers Astronuc! And thanks for the help everyone!
     
  15. Jan 2, 2010 #14

    HallsofIvy

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    It would have helped if you had told us that to begin with! You said "factor one trillion" and that usually means into integer factors.
     
  16. Jan 2, 2010 #15

    FeDeX_LaTeX

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    Try this: Factor 611939 into two different integer factors. ;)

    ^^
     
  17. Jan 2, 2010 #16

    Astronuc

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    You're welcome. I was wondering if one had to have integers which would be impossible given the constraints. I just start dividing 512 by 2 until I found a number without zeros.

    On the other hand, one can also divide 212 by 5's, in which case only one division is needed 212/5 = 819.2 and 48828125 = 511.
     
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