if n=2^2x3^2x7 and m is a natural number,how many possible values can m have at the most such that n/18m is a whole number?

n/18m

= (2^2x3^2x7)m/18
= 2x7m
= 14m
since m is a natural number,
14m is always a whole number.

did you mean:
n/(18m) ?
make the necessary changes.