Is the modulus congruent with 0 (zero)?

Question

Is it true that, given that I have a modulus m, then m is congruent with 0?

My reason for thinking that this is the case is the observation that for any integer k, then

$\ km \ (mod \ m) \cong \ 0 $

Since the residue (remainder) when a number is divided by a multiple of the modulus would be 0.

Answer 1

$km$ ($mod$ m) means remainder of $km$ divided by $m$.
so $\frac{km}{m}\equiv0$ ($mod$ $m$).