Dumb Question: When Factoring Do We List Negative Factors?

Click For Summary
SUMMARY

In mathematics, factorization is conventionally defined for positive numbers, which is why only positive factors are typically listed. For example, while -2 is indeed a factor of -4, the standard practice is to factor the positive equivalent, such as 4 being factored as 2 and 2. Allowing negative factors would violate the uniqueness of prime factorization, as prime numbers are defined to be greater than 1. Therefore, the exclusion of negative factors is an established convention in mathematical factorization.

PREREQUISITES
  • Understanding of basic factorization concepts
  • Familiarity with prime numbers and their properties
  • Knowledge of positive and negative integers
  • Basic mathematical notation and terminology
NEXT STEPS
  • Research the properties of prime numbers and their significance in number theory
  • Explore the concept of unique factorization in the context of integers
  • Learn about the implications of negative numbers in mathematical operations
  • Study advanced factorization techniques, including polynomial factorization
USEFUL FOR

Students, educators, and anyone interested in understanding the conventions of mathematical factorization and the properties of prime numbers.

bballwaterboy
Messages
85
Reaction score
3
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!
 
Mathematics news on Phys.org
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!
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 9 ·
Replies
9
Views
3K
Replies
45
Views
7K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 10 ·
Replies
10
Views
3K
  • · Replies 28 ·
Replies
28
Views
3K