Anonymous
Anonymous asked in Science & MathematicsMathematics · 9 years ago

How many whole numbers from 1 to 100 are divisible by 3 different prime numbers?

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  • Anonymous
    9 years ago
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    Note: Zero and 1 are not considered prime numbers!

    Prime numbers = {2,3,5,7,11,13, 17,...}

    2*3*5 = 30

    2*3*7 = 42

    2*3*11 = 66

    2*3*13 = 78

    Other combinations would yield number greater than 100.

    Answer: 4

  • Anonymous
    9 years ago

    You may want to think about doing this by brute force.

    Here is your first number: 2x3x5=30. 30 is divisible by three different prime numbers and it is a whole number in the set {1, 2, 3,...,100}

    Can you see that you can continue this process by changing the 5 for a 7 then 11 then ?

    Can you see that you won't really have a lot of work because at some point very soon, you will exceed 100?

    An advanced student might consider combinations of the products of primes directly.

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