2024/056) How do I find the minimum positive integer $n>114$, such that $2001 \equiv 114(\mod n)$

It is 114 mod n so 2001–114 should be divisible by n and $n > 114$

Factors of 1887 are 1 3 17 37 51 111 629 1887. any number $<= 111$ shall give a smaller remainder and 2 numbers 629 and 1187 shall give a remainder 114 so the number is lower of the 2 that is 629.