Question

Is 0 a multiple of any no, since any no time 0 is always zero ?

Answer 1

Definition of multiple: \( a \) is a multiple of \(b \) if there exists another integer \(c\) such that \( a = b \times c \) where \( a,b,c \in \mathbb{Z} \)

Lets put \( a=0\) and \(b\) any integer, then now we need to find an integer \( c\) such that \( 0 = b\times c\). Notice that if we choose \( c = 0\) the claim holds, Hence, \(0\) is a multiple of every integer. QED.