Basic Mathematics for College Students

1.7 Prime Factors and Exponents 81

EXAMPLE (^2) Factor 40 using: a.two factors b.three factors
StrategyWe will find a pair of whole numbers whose product is 40 and three
whole numbers whose product is 40.
WHYTo factora number means to express it as the product of two (or more)
numbers.
Solution
a.To factor 40 using two factors, there are several possibilities.
and
b.To factor 40 using three factors, there are several possibilities. Two of them are:
40  5  4  2 and 40  2  2  10

40  1 40, 40  2 20, 40  4 10, 40  5  8

Self Check 2

Factor 18 using: a.two factors

b.three factors

Now TryProblems 39 and 45

EXAMPLE (^3) Find the factors of 17.
StrategyWe will find all the pairs of whole numbers whose product is 17.
WHYEach of the numbers in those pairs is a factor of 17.
Solution
The only pair of whole numbers whose product is 17 is:
Therefore, the only factors of 17 are 1 and 17.

1  17  17

Self Check 3

Find the factors of 23.

Now TryProblem 49

2 Identify even and odd whole numbers, prime numbers,

and composite numbers.

A whole number is either evenor odd.

Even and Odd Whole Numbers

If a whole number is divisible by 2, it is called an evennumber.

If a whole number is not divisible by 2, it is called an oddnumber.

The even whole numbers are the numbers

The odd whole numbers are the numbers

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, p

0, 2, 4, 6, 8, 10, 12, 14, 16, 18, p

The three dots at the end of each list shown above indicate that there are infinitely
many even and infinitely many odd whole numbers.

The Language of Mathematics The word infinitelyis a form of the word

infinite, meaning unlimited.

In Example 3, we saw that the only factors of 17 are 1 and 17. Numbers that
have only two factors, 1 and the number itself, are called prime numbers.