The numbers $11284$ and $7655$ when divided by a certain number of three digits, leave the same remainder. find that three digit number.

If we divide $11284$ and $7655$ by their difference the remainder will be the same.
Hence $11284-7655=3629$
The factors of $3629$ are $19$ and $191.$

$19\times 191=3629$
Here the only $3$ digit number is $191.$
Hence the required three digits number is $191.$