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Math Help - Difficult problem solving quesiton

  1. #1
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    Difficult problem solving quesiton

    Hello Mathwizards!

    I have a problem solving question that is basically this-

    "Find the greatest factor of 11! that is one greater than a multiple of 6"
    That's all it gives you
    I already know that 11!=39,916,800

    And I think that the answer is 385. However I am unsure how to word it or show how I done it.
    The way I worked it out was to use a factor calculator online to find all the factors of 11! and then subtracted 1 then divided by 6. If this gave a whole number then this is a possibility. I did this for all odd factors as I fathomed that 1 greater than a multiple of 6 must be odd as a multiple of 6 will always be even.
    This seems like a tedious process and I am sure that there must be an easier method.

    I tried creating equations with x=a factor of 11! and y=a multiple of 6 but the only two I could get were
    x-1=y
    x=y+1

    I have to display full working and I dont want to say that I have done that the method above for hundreds of numbers.

    Any help or even pointers in the right direction would be GREATLY appreciated.

    Thanks in advance,
    Danny
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  2. #2
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    Re: Difficult problem solving quesiton

    Thank you for replying skeeter

    But would the factors of 11! not be all the factors of 39,916,800?
    So for example 19,958,400 would be a factor as this multiplied by 2 is 11!
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