sentences:  For example, the fact that positive numbers have unique factorizations means that one can determine whether a number has an even or odd number of distinct prime factors.Since 1 is not prime, nor does it have prime factors, it is a product of 0 distinct primes; since 0 is an even number, 1 has an even number of distinct prime factors.This implies that the Möbius function takes the value , which is necessary for it to be a multiplicative function and for the Möbius inversion formula to work.