Adding to what amelius said. The formal term for the algebraic system we are talking about is ring. We want to consider all the elements of the ring to be num

Adding to what amelius said. The formal term for the algebraic system we are talking about is ring. We want to consider all the elements of the ring to be numbers since they are all part of the same algebraic system. Also, let’s broaden the perspective a bit and think about rational numbers. These include all integers and within the system of rational numbers every nonzero element is a unit. So 2 which is prime within the ring of integers is no longer prime within the ring of rational numbers. Every rational number is a multiple of 2 in the sense of 2*(a/2) = a The notion of primality is not a property of a number it is a property of a number within the structure of a ring. We don’t want to think of units as not being numbers. Also, the construction of natural numbers is such that 1 is the successor of 0. It just happens that when considering the operation of multiplication 1 is a unit but this is happenstance and not a reason to exclude 1 as a number. It’s worth noting that under addition 0 is a “unit” (really identity but plays additive role that 1 does under multiplication).