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Math Help - Please help us answer this 11+ question

  1. #1
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    Please help us answer this 11+ question

    Hi, .
    Please see below a question on my 11 year old daughter's exam paper that we have no idea of the answer.

    Find two numbers which when multiplied together make a thousand. neither of the two numbers must use any zeros.

    Then, find two numbers which when multiplied together make a million. again neither of the two numbers must use any zeros.

    Is there a quick way to do this rather then guess numbers a multiply them?

    Thanks
    Alvina
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  2. #2
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    Quote Originally Posted by dee@landspace.co.uk View Post
    Hi, .
    Please see below a question on my 11 year old daughter's exam paper that we have no idea of the answer.

    Find two numbers which when multiplied together make a thousand. neither of the two numbers must use any zeros.

    Then, find two numbers which when multiplied together make a million. again neither of the two numbers must use any zeros.

    Is there a quick way to do this rather then guess numbers a multiply them?

    Thanks
    Alvina
    If you look at all the factor of 1000

    1000 = 2^3 5^3 = 2 \times 2 \times 2 \times 5 \times 5 \times 5

    then pick three and three such that the product of each have no zeros. The same goes for the next problem.
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  3. #3
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    Dear dee@landspace.co.uk,

    I suppose that we talk about positive integer numbers.
    Divide up 1000 into prime numbers:
    1000 = 10*10*10 = 2*2*2*5*5*5.
    We have to componate two groups so that the two numbers have not any zeros. Zero will appear if the number containts 2 and 5 together. Therefore the one number = 2*2*2 the other = 5*5*5.
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  4. #4
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    Thank you very much indeed for solving this question . you made it look really easy. Thanks

    Deee
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