find the value of z for which the number 471z8 is divisible by 9​

Question

find the value of z for which the number 471z8 is divisible by 9​

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Abigail 3 months 2021-11-02T18:19:27+00:00 1 Answer 0 views 0

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    2021-11-02T18:21:10+00:00

    A number is exactly divisible by 9 if and only if the sum of its digits is exactly divisible by 9.

    The sum of digits of the number 471z8 is,

    \displaystyle\longrightarrow\sf{s=4+7+1+z+8}

    \displaystyle\longrightarrow\sf{s=z+20}

    Here z is a non – negative one digit number. And s should be exactly divisible by 9.

    There’s only one possible value for s.

    \displaystyle\longrightarrow\sf{s=27}

    \displaystyle\Longrightarrow\sf{z=27-20}

    \displaystyle\longrightarrow\sf{\underline {\underline {z=7}}}

    Hence 7 is the answer, and our number is 47178.

    • 47178 = 9 × 5242

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