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Math for Educators

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I am thinking of some #s less than 100. When I divide them by 2 there is a remainder of 1. When I divide them by 3 there is a remainder of 1. When I divide it by 4 there is a remainder of 1. However, when I divide by 5 there is no remainder. what are the #'s?

- my answer so far is every number ending in a zero or five from 1-100 but I don't think its that simple. If someone could help me figure this out it would be greatly appreciated!

  • Math for Educators -

    The statement, "when I divide them by 2, there is a remainder of 1" means that the numbers must be odd, therefore they can't end in a 0. I'm only seeing 2 answers, 25 and 85

  • Math for Educators -

    like Joe said, the first condition limits you to odd numbers
    the second condition limits you to the numbers
    7 13 19 25 31 37 43 49 55 61 67 73 79 85 91 97 (every odd multiple of 3 + 1)
    the third condition limit you to the numbers
    5 9 13 1721 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 ( every multiple of 4 + 1)
    the fourth conditon gives you
    5 15 25 35 45 55 65 75 85 95

    As Joe pointed out , the only numbers fitting all 4 conditions are
    25 and 85

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