Question

find the largest five digit number which when divided
by 8 and 9 leaves the same remainder 5

Answer 1

Answer:

lcm of (8,9)=72

the greatest no. of 5 digit is 99999

now, (99999÷72) then we get 63 reminder , 1st we have to subtract the remainder in 99999 and add 5

so resultant no. is = 99999-63+5=99941

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Answer 2

Question :-

find the largest five digit number which when divided

by 8 and 9 leaves the same remainder 5

Solution :-

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 : -

8 = 2 × 2 × 2

9 = 3 × 3

LCM = 2 × 2 × 2 × 3 × 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: -

$\begin{gathered}\begin{gathered}72 \: \: {\begin{array}{|c} 1388\\ \frac{\qquad \qquad}{} \\ 99999 \\ - 72 \: \: \: \: \: \: \: \: \: \\ \frac{\qquad \qquad}{} \\279 \: \: \: \: \: \: \\ - 216 \: \: \: \: \: \\\frac{\qquad \qquad}{} \\ 639 \: \: \: \\ - 576 \: \: \: \: \: \: \\ \frac{\qquad \qquad}{} \\ 639 \\ - 576 \: \: \: \\\frac{\qquad \qquad}{} \\ 63 \end{array}} \\ \end{gathered}\end{gathered}$

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

∵ 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.

Hence,

Answer :-

• 99941

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