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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- Oct 13th 2012, 07:57 AM #1

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- Oct 14th 2012, 11:26 AM #2

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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 $\displaystyle 0.$