


Description 



Factors: When two or more integers are multiplied, each number is a factor of the product. "To factor" means to write the number or term as a product of its factors. 
Examples of Factors and Proper
Factors
15 = 3 x 5, so 3 and 5 are factors of 15. Also, 15 = 1 x
15, 1 and 15 are factors of 15. Therefore, 15 has four positive factors: 1, 3,
5, 15. When factors are multiplied together, the result is a product. For
example, 3 x 5 results in the product 15.
Many textbooks assume that when you look for factors, you only
consider the positive factors. But what about negative factors? You can multiply
1 and 15 to produce +15 and 3 and 5 to get +15. So, including both postive
and negative factors, the factors of 15 are : ±1, ±3, ±5, ±15.
Many textbooks assume that proper factors are positive factors
that are less than the number itself. We will also consider only positive
factors when we are looking for proper factors because of our definitions of perfect numbers, deficient numbers, abundant numbers, amicable numbers. Thus, the
proper factors of 15 are the positive factors of 15 that are less than 15
itself: 1, 3, and 5.
The factors of 6 are ±1, ±2, ±3, and ±6. The proper
factors are 1, 2, and 3.
What are the factors of 36? (Assume we want both
positve and negative factors.)
36 = 1 x 36 
36 = 2 x 18 
36 = 3 x 12 
36 = 4 x 9 
36 = 6 x 6 
36 = 1 x 36 
36 = 2 x 18 
36 = 3 x 12 
36 = 4 x 9 
36 = 6 x
6 
So, the factors of 36
are ±1, ±2, ±3, ±4, ±6, ±9, ±12 ,±18, ±36. What are the proper factors of
36?
Nonexample of Factors
Since 3 does not divide 4 exactly, then 3 is not a
factor of 4.


