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Math Help - How many six-digit positive integers are there, which is evenly divisible by 4 or 9?

  1. #1
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    Wink How many six-digit positive integers are there, which is evenly divisible by 4 or 9?

    How many six-digit positive integers are there, which is evenly divisible by 4 or 9?

    (If you let A be the amount of six-digit positive integers that are evenly divisible by 4 and B be the amount of six-digit positive integers that are evenly divisible by 9, so you should therefore
    determine the number of elements in A ∪ B.
    Remember that A and B in this case may not be disjoint sets.)

    /Monica
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  2. #2
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    Quote Originally Posted by Monika1987 View Post
    How many six-digit positive integers are there, which is evenly divisible by 4 or 9?

    (If you let A be the amount of six-digit positive integers that are evenly divisible by 4 and B be the amount of six-digit positive integers that are evenly divisible by 9, so you should therefore
    determine the number of elements in A ∪ B.
    Remember that A and B in this case may not be disjoint sets.)

    /Monica
    How many such numbers are divisible by 4? How many such numbers are divisible by 9? How many such numbers are divisible by 4*9= 36?

    Are we to assume that by "six-digit positive numbers" you mean numbers from 100000 to 999999?
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  3. #3
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    yes. By six-digit number they want to know from 100000-999999 how many numbers there are that is evenly divisible by 4 or 9.
    example:
    444444 and 999999 is such numbers. so how many between 100000-999999?
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  4. #4
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    Hello, Monika1987!

    How many 6x-digit positive integers are there that are evenly divisible by 4 or 9?
    There are 900,000 six-digit numbers.

    Every 4th number is divisible by 4: . \frac{900,\!000}{4} \:=\:225,\!000 numvbers divisible by 4.

    Every 9th number is divisible by 9: . \frac{900,\!000}{9} \:=\:100,\!000 numbers divisible by 9.

    But every 36th number is divisible by both 4 and 9: . \frac{900,\!000}{36} \:=\:25,\!000


    \text{Therefore: }\;225,\!000 + 100\!,000 - 25,\!000 \;=\;\boxed{300,\!000}\,\text{ numbers divisible by 4 or 9.}

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