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number less than 200 sum of the digit is 6 product of the digit is 0 each factor of 75 is its factor too?

  • math -

    yes

  • math -

    I'd say no.

    The prime factors of 75 are 3 and 5
    All the factors of 75 are 3,5,15,25

    Write n = abc

    Since the product of the digits is zero, one of the digits is zero.

    Since the sum of the digits is 6, the number is 9k+6 for some k.

    That means that 3 is a factor of n

    Now, abc is either

    105 or 150

    3,5,15 are factors of both. 25 does not divide 105.

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