49 For naturals n and m , we can express the statement ¡° n is a factor of m ¡± formally as follows:
m: n¡Ánat
(a) What are the factors of 0 ?
¡ì For any natural n we have 0: n¡Ánat , so all naturals are factors of 0 . (b) What is 0 a factor of?
¡ì m: 0¡Ánat requires m to be 0 , so 0 is a factor of only 0 . (c) What are the factors of 1 ?
¡ì 1: n¡Ánat requires n to be 1 , so only 1 is a factor of 1 .
(d) What is 1 a factor of?
¡ì For any natural m we have m: 1¡Ánat , so 1 is a factor of all naturals.