Basic Mathematics for College Students

80 Chapter 1 Whole Numbers

SECTION 1.7

Prime Factors and Exponents

Objectives

1 Factor whole numbers.

2 Identify even and odd whole

numbers, prime numbers, and

composite numbers.

3 Find prime factorizations using

a factor tree.

4 Find prime factorizations using

a division ladder.

5 Use exponential notation.

6 Evaluate exponential

expressions.

In this section, we will discuss how to express whole numbers in factored form. The

procedures used to find the factored form of a whole number involve multiplication

and division.

1 Factor whole numbers.

The statement has two parts: the numbers that are being multiplied and the

answer. The numbers that are being multiplied are called factors,and the answer is

the product.We say that 3 and 2 are factors of 6.

3  2  6

Factors

Numbers that are multiplied together are called factors.

EXAMPLE (^1) Find the factors of 12.
StrategyWe will find all the pairs of whole numbers whose product is 12.
WHYEach of the numbers in those pairs is a factor of 12.
Solution
The pairs of whole numbers whose product is 12 are:
and
In order, from least to greatest, the factors of 12 are 1, 2, 3, 4, 6,and 12.

1  12 12, 2  6 12, 3  4  12

Self Check 1

Find the factors of 20.

Now TryProblems 21 and 27

Success Tip In Example 1, once we determine the pair 1 and 12 are factors of

12, any remaining factors must be between1 and 12. Once we determine that

the pair 2 and 6 are factors of 12, any remaining factors must be between2 and

6. Once we determine that the pair 3 and 4 are factors of 12, any remaining
   factors of 12 must be between3 and 4. Since there are no whole numbers
   between 3 and 4, we know that all the possible factors of 12 have been
   found.

In Example 1, we found that and are the factors of 12. Notice

that each of the factors divides 12 exactly, leaving a remainder of 0.

In general, if a whole number is a factor of a given number, it also divides the given

number exactly.

When we say that 3 is a factor of 6, we are using the word factoras a noun. The

word factoris also used as a verb.

12

12

 1

12

6

 2

12

4

 3

12

3

 4

12

2

 6

12

1

 12

1 , 2 , 3 , 4 , 6 , 12

Factoring a Whole Number

To factora whole number means to express it as the product of other whole

numbers.