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17 January, 09:36

Tom thought of a natural number, multiplied all its digits and after that he multiplied the result by the initial number. Is it possible to get 1716 as a result?

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  1. 17 January, 09:52
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    All of these operations result in natural numbers, so let's consider all divisor pairs of 1716:

    (1, 1716)

    (2, 858)

    (3, 572)

    (4, 429)

    (6, 286)

    (11, 156)

    (12, 143)

    (13, 132)

    (22, 78)

    (26, 66)

    (33, 52)

    (39, 44)

    The divisor pair (12, 143) fits the bill, since the product of the digits of 143 is 1*4*3 = 12, so the answer is yes.
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