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# Negative integers

The absolute value of a negative integer is the number multiplied by −1. The set of all negative integers may be denoted ${\displaystyle \mathbb {Z} ^{-}}$. And so we may write for ${\displaystyle n\in \mathbb {Z} ^{-}}$ that ${\displaystyle |n|\in \mathbb {Z} ^{+}}$.
The study of prime numbers is generally unconcerned with negative integers. But the question does occasionally arise: how do you write the factorization of a negative integer? A number of different solutions suggest themselves, for example, ${\displaystyle -48=-(2^{4})\times 3=(-2)^{4}\times -3=2^{4}\times -3=\ldots }$, etc., but these are unsatisfactory on account of the seemingly arbitrary sign choices. To insure uniformity, the factorization of a negative integer could be expressed as −1 followed by the factorization of the absolute value, e.g., ${\displaystyle -48=(-1)\times 2^{4}\times 3}$.