# Is -3 a multiple of 3?

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This is part of a series on common misconceptions.

True or False?$-3$ is a multiple of $3.$

**Why some people say it’s true:** It’s $-1\times 3.$

**Why some people say it’s false:** Negative numbers aren't multiples, just as they aren't primes.

The statement is $\color{#20A900}{\textbf{true}}$.

Explanation:It is valid to multiply -1 by 3, get -3, and thus conclude -3 is a multiple of 3. Negative numbers can be multiples and it is valid to multiply them, so since -1 times 3 is -3, it follows that -3 is a multiple of 3. $_\square$

Rebuttal: This doesn’t work! You can’t multiply a negative. And even if you could, negative numbers can’t be primes nor composites, so they can’t be multiples.

Reply: You can multiply negatives and $-1\times 3=-3$ is valid. Normal mathematical logic implies that -3 is a multiple of 3. While negative numbers are neither primes nor composites, this does not mean they can’t be multiples. For instance, 0 is neither a prime nor a composite, yet it has an infinite amount of factors. 0.5 is a multiple of 0.5, yet it is neither prime nor composite.There is an incredibly big group of numbers like this, yet their having factors, while possible, is not always well-defined.

**Cite as:**Is -3 a multiple of 3?.

*Brilliant.org*. Retrieved from https://brilliant.org/wiki/negative-multiples/