Question & Answer
QUESTION

Which is the greatest five digit number exactly divisible by 279 ?
$
  A{\text{ 99603}} \\
  B{\text{ 99837}} \\
  {\text{C 99882}} \\
  {\text{D None}} \\
 $

ANSWER Verified Verified
Hint- In order to solve this question, we will take the greatest five digit number and then divide the number with the given divisor. This will give the remainder and we can further use it to calculate the required result.

Complete step-by-step answer:
As we know that the greatest five digit number is 99999 because adding 1 will give the six digit number.
Now we will divide this number by the given divisor which is 279.
$ \Rightarrow $ $\dfrac{{99999}}{{279}}$
$ \Rightarrow
$we get 358 as quotient and 117 as remainder.
$ \Rightarrow $As we did not get the remainder as zero which verifies that it is exactly divisible so we will subtract the remainder from the greatest number in order to get the exact divisible greatest five digit number.
$ \Rightarrow $99999-117
$ \Rightarrow $99882
This shows that if we divide 99882 by 279, it will be exactly divided.
$\therefore $ Option C is correct.

Note- In order to solve this type of question, one must know that the remainder of the exact divisible number should be zero like we did in the question. Also the same method can be used for greatest three digit number and greatest four digit number.