Dumb Question: When Factoring Do We List Negative Factors?

  • #1

Main Question or Discussion Point

I only see positive factors in my book. Example: 2 and 2 are factors of 4. But aren't -2 and -2?

Is there some unspoken rule in math that only positive factors count? Thanks!
 

Answers and Replies

  • #2
PeroK
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There is no advantage in considering negative factors. So, factorisation is generally defined for positive numbers. If n is negative (-10, say), then -n is positive. So, you simply factorise -n and then put a minus sign in front:

-10 = -(10) = -(2)(5)

The main problem if you allowed negative factors would be that you no longer have uniqueness of the prime factorisation. This is why the definition of a prime number (p) includes the condition that p > 1.

So, essentially this is an unspoken rule as nobody notices it very often!
 

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