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Thread: Find the number of integers

  1. #1
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    Find the number of integers

    Find the number of integers from 1 to 10,000 which are divisible by either 13 or 51
    regards
    Sridhar
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  2. #2
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    Hello yshridhar

    Welcome to Math Help Forum!
    Quote Originally Posted by yshridhar View Post
    Find the number of integers from 1 to 10,000 which are divisible by either 13 or 51
    regards
    Sridhar
    $\displaystyle 10,000\div13 = 769.1$, so there are $\displaystyle 769$ integers from $\displaystyle 1$ to $\displaystyle 10,000$ that are divisible by $\displaystyle 13$.

    In the same way, you can find the number of integers that are divisible by $\displaystyle 51$.

    Add this number to $\displaystyle 769$. Then you will need to subtract the number of integers that are divisible by $\displaystyle 13\times51\; (= 663)$, because they will have been counted twice. (Note that $\displaystyle 51 = 3 \times 17$, so $\displaystyle 51$ and $\displaystyle 13$ have no common factors.)

    Can you complete this now?

    Grandad
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  3. #3
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    Thank you Grandad
    regards
    Sridhar
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