how do we find the least residue of

Question

1789 (mod 4), (mod 10), (mod 101)

Answer 1

I think I understand your question.
The mod(x,z) function says divide x by z and give the remainder. (does remainder mean "residue" in your question?)
So, mod(1789,4) is 447 and 1 remainder.
mod(1789,10) is 178 and 9 remainder.
mod(1789,101) is 17 and 72 remainder.