Every Natural number can be written as the product of at least one pair of factors, 1 times the number itself. When a Natural number has exactly one factor pair, it is prime. All other Natural numbers, called composite, have more than one factor pair.

Being able to find the factor pairs for a number will make factoring polynomials easier. The following exercise provides an opportunity to practice a skill that you will need for Unit V: Polynomials and Factoring.

Product: the result of multiplication
Factor: a number being multiplied
Sum: the result of addition

Find the factor pair for each number that has the given sum.

Example:
Product   36

factor    ?
factor    ?

Sum        15

The factor pairs of 36 are:        and the sum of each pair is:
       1 * 36                                                 37
       2 * 18                                                 20
       3 * 12                                                 15    this sum has the factor pair 3, 12
       4 *   9                                                 13
       6 *   6                                                 12

So we fill in the factor spaces on our chart with 3 and 12:
Product        36

factor         3
factor       12

Sum             15

Exercises

Product	36	5	24	9	75	68	72	18	51
factor
factor
Sum	13	6	11	-6	20	36	-22	11	20

HINT: The product of two numbers having the same sign is always positive.
The sum of two numbers having the same sign has that sign.

Answers to Exercises:

Product	36	5	24	9	75	68	72	18	51
factor	4	1	3	-3	5	2	-4	2	3
factor	9	5	8	-3	15	34	-18	9	17
Sum	13	6	11	-6	20	36	-22	11	20