Smallest Number which is Multiplied by 99 by Appending 1 to Each End

Theorem
The smallest positive integer which is multiplied by $99$ when $1$ is appended to each end is:
 * $112 \, 359 \, 550 \, 561 \, 797 \, 732 \, 809$

Proof
We have that:


 * $112 \, 359 \, 550 \, 561 \, 797 \, 732 \, 809 = 7 \times 11 \times 61 \times 87 \, 629 \times 337 \, 411 \times 809 \, 063$

while: