Question

Find the greatest number of 5 digits, that will give a remainder of 5, when divided by 8 and 9 respectively.

Answer 1

Hint: We know that the greatest 5 digit number is 99999, but we have to find the greatest 5 digits number that will give remainder of 5, when divided by 8 and 9 respectively. For this we take L.C.M of 8 and 9 and divide the number 99999.

Complete step-by-step answer:

We know that the greatest 5 digit number is 99999.

Now, we have to find the greatest 5 digit number that will give a remainder of 5, when divided by 8 and 9 respectively.

So, L.C.M of 8 and 9 is shown below: -

\[\begin{align}

  & 8=2\times 2\times 2 \\

 & 9=3\times 3 \\

\end{align}\]

L.C.M = \[2\times 2\times 2\times 3\times 3=72\].

Hence, the L.C.M of 8 and 9 is 72.

Now, we will find the greatest 5 – digit number divisible by 8 and 9 by dividing 99999 by 72.

The division of 99999 by 72 is shown as below: -

\[72\overset{1388}{\overline{\left){\begin{align}

  & 99999 \\

 & \underline{-72} \\

 & 279 \\

 & \underline{-216} \\

 & 639 \\

 & \underline{-576} \\

 & 639 \\

 & \underline{-576} \\

 & 63 \\

\end{align}}\right.}}\]

So, from the above division we get,

Quotient = 1388

Remainder = 63

So, the greatest 5 – digit number divisible by 8 and 9 = 99999 – 63 = 99936.

Required number = 99936 + 5 = 99941

\[\because \] We have been given that a remainder of 5 is there when the number is divided by 8 and 9 respectively. So, we add the remainder to the number which is divisible by 8 and 9.

Therefore, we get the greatest number of 5 digits, that will give a remainder of 5, when divided by 8 and 9 respectively is 99941.


Note: Just be careful while doing calculation as there is a chance that you might make a mistake and you will get the incorrect answer. Most students make the mistake of adding the remainder to 99999 instead of subtracting it. Also, they may forget to add 5 to 99936 and often write 99936 as the final answer.