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Math Help - just a simple question

  1. #1
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    just a simple question

    how many factors of 1000 can be divided by 20 without a remainder.

    all u do is 20 goes into 1000 50 times so ur answers 50 rite? and another questions im doing a couple of different questions do i need to put them all on the same post xD
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by xsriel View Post
    how many factors of 1000 can be divided by 20 without a remainder.

    all u do is 20 goes into 1000 50 times so ur answers 50 rite? and another questions im doing a couple of different questions do i need to put them all on the same post xD
    To your last question...no don't

    Ok so think about it 1000=2^35^3

    So the factors are \left\{2,4.8,5,25,125,50,200,\cdots\right\}

    I think you can see what to do from there
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  3. #3
    Senior Member euclid2's Avatar
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    Quote Originally Posted by xsriel View Post
    how many factors of 1000 can be divided by 20 without a remainder.

    all u do is 20 goes into 1000 50 times so ur answers 50 rite? and another questions im doing a couple of different questions do i need to put them all on the same post xD
    Your final outcome should be 6.
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  4. #4
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    I don't get how u get 6......... ?
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  5. #5
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    first, list the factors of 1000
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by euclid2 View Post
    Your final outcome should be 6.
    i agree.

    taking mathstud's lead, i want to flesh this out a little more. i also found the prime factorization of 1000, then i factored 20 out of it. we want all possible multiples of 20 from this factorization and of course, 20 itself.

    so 1000 = 2 \cdot 5^2 \cdot 20

    now how many different combinations can you have in front of the 20? and of course, 1 \cdot 20 is an additional one
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  7. #7
    Senior Member euclid2's Avatar
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    Quote Originally Posted by Jhevon View Post
    i agree.

    taking mathstud's lead, i want to flesh this out a little more. i also found the prime factorization of 1000, then i factored 20 out of it. we want all possible multiples of 20 from this factorization and of course, 20 itself.

    so 1000 = 2 \cdot 5^2 \cdot 20

    now how many different combinations can you have in front of the 20? and of course, 1 \cdot 20 is an additional one
    Absolutely, this is what i did, thanks!
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  8. #8
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    oh so i only do the factors infront of 20? not 1 or 2 cause like u can do 1 divided by 20 rite? u just add zeros? sry ima dumb 7th grader xD
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  9. #9
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by euclid2 View Post
    Absolutely, this is what i did, thanks!
    great minds think alike

    Quote Originally Posted by xsriel View Post
    oh so i only do the factors infront of 20? not 1 or 2 cause like u can do 1 divided by 20 rite? u just add zeros? sry ima dumb 7th grader xD
    huh? i don't get what you are saying

    the point is, to be divisible by 20, you must be an integer times 20, thus, we only care about the factors that are a multiples of 20

    now that i think about it, should we not consider negative factors as well?
    Last edited by ThePerfectHacker; October 30th 2008 at 11:24 AM.
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  10. #10
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    yeah thats what im asking, what about factors behind 20
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  11. #11
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    xsriel, if you don't understand that, then look at it this way. You should know how to list the factors of 1000. They are 1 2 4 5 8 10 20 25 40 50 100 125 200 250 500 1000 . Which ones are divisible by 20 with no remainder? 20, 40, 100, 200, 500, 1000. That makes six. Maybe that will make it more clear to you.
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  12. #12
    Senior Member euclid2's Avatar
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    Quote Originally Posted by xsriel View Post
    yeah thats what im asking, what about factors behind 20
    we can think of 1000 as 20*50. The factors of 50 are 1,2,5,10,25, and 50. If we multiply each of these 6 factors of 50 by 20, we will get the 6 factors of 1000 that can be divided evenly by 20.

    Therefore, the factors are 20,40,100,200,500, and 1000.

    hope this helps.
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  13. #13
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    OHHHHHHHHHHHHHHHHHHHHH XXXXXDDDDDDDD ty
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