If i have a big number, like:
$39486432$ or $485921157$
And they ask me, with what number when dividing it, is it left with less residue? If you take into account the exact divisors. I would not like to use brute force, is there a wonderful theorem or approach to this?
Graphically: $\frac{485921157}{n}$, get the $n$ with less residue, without take into account the $0$ residue.
Presumably a good answer, for a large number $n$, is "Divide it by $n-1$; that'll give a remainder of 1, which is as small as possible while not being zero."
Thus in one of your examples, we have $$ \frac{ 485921157}{ 485921156} = 1 \text {with a remainder of $1$}. $$