Why does every number have 1 as a proper factor?

Answer 1

Every number has one as a factor because one can divide into any number with no remainder. Every number does not have one as a proper factor because the set of proper factors does not contain one and the number itself.

Answer 2

They are not the same.

A factor of a number is any number that divides into the number exactly, that is without remainder.

The number itself divides exactly into itself and so is a factor of the number.

The set of proper factors of a number is all factors of the number except itself.

For example:

• The factors of 24

{1, 2, 3, 4, 6, 8, 12, 24}

• The proper factors of 24

{1, 2, 3, 4, 6, 8, 12}

Note: Some definitions of the proper factors of a number exclude 1 as well.