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Thread: my weakness in math - need help

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    my weakness in math - need help

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    I have a grave weakness in math. Consider the following questions.

    Of the positive integers that are multiples of 30 and are less than or equal to 360, what fraction are multiples of 12?

    I know that prime factorization is involved in solving such questions but I don't know the rules regarding prime factorization. I know how to find the prime factorization of numbers but have no idea how to solve such questions. Please help.

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    Re: my weakness in math - need help

    1. If you do not know what to do, you can in this case write all numbers and check one by one. This is clearly only an option if you have no idea what to do.

    2. Now, a more practical answer: A multiple of 30 can be written 30*k. You need 12 to divide 30*k that is only possible if k is multiple of 2. This is because 12 has two 2's in its factorization and 30 only one. You are considering 12 numbers namely 30*1,30*2,30*3,...,30*12 (any other is greater than 360, not multiple of 30 or not positive). That is k = 1,2,3,...,12 and you want to know which of them are multiple of 2. These are 2,4,6,8,10,12 that is 6 numbers of 12... that means 50% of the numbers or 1/2.

    I tried to keep my solution simple but understandable. I hope it is both.

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