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Thread: Help please

  1. #1
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    India
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    Help please

    First 44 nos are written in order to form largest no N=12345678910111213.........424344.
    What will be remainder when N is divided by 45??
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Re: Help please

    Hello, guest13!

    $\displaystyle \text{The first 44 numbers are written in order to form this large number:}$
    . . . . . $\displaystyle N\;=\;12345678910111213\,\hdots\,424344.$

    $\displaystyle \text{What will be the remainder when }N\text{ is divided by }45\,?$

    Here are two hints.
    Let's see how far you get with them.


    (1) When $\displaystyle N$ is divided by 5, the remainder is $\displaystyle 4.$


    (2)The sum of the digits of $\displaystyle N$ is $\displaystyle 270.$
    . . Since 270 is divisible by 9, $\displaystyle N$ is divisible by 9.
    . . Hence, when $\displaystyle N$ is divided by 9, the remainder is $\displaystyle 0.$
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