Basics

you’re mixing definitions a bit

multiple:

a multiple of a number n is of the form n × k, where k is any integer

so for 7 → 7×0 = 0, so yes, 0 is a multiple of every number

factor:

a factor of n is a number that divides n exactly

since division by 0 is undefined, 0 cannot be a factor of any number

so final:

0 is a multiple of every number

0 is not a factor of any number