Basic Mathematics for College Students

82 Chapter 1 Whole Numbers

Prime Numbers

A prime numberis a whole number greater than 1 that has only 1 and itself as

factors.

The prime numbers are the numbers:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101,

There are infinitely many prime numbers.

p

Note that the only even prime number is 2. Any other even whole number is

divisible by 2, and thus has 2 as a factor, in addition to 1 and itself. Also note that not

all odd whole numbers are prime numbers. For example, since 15 has factors of 1, 3,

5, and 15, it is not a prime number.

The set of whole numbers contains many prime numbers. It also contains many

numbers that are not prime.

Composite Numbers

The composite numbersare whole numbers greater than 1 that are notprime.

The composite numbers are the numbers

There are infinitely many composite numbers.

4, 6, 8, 9, 10, 12, 14, 15, 16, 18, p

Caution! The numbers 0 and 1 are neither prime nor composite, because

neither is a whole number greater than 1.

EXAMPLE (^4) a. Is 37 a prime number? b. Is 45 a prime number?
StrategyWe will determine whether the given number has only 1 and itself as
factors.
WHYIf that is the case, it is a prime number.
Solution
a.Since 37 is a whole number greater than 1 and its only factors are 1 and 37, it is
prime. Since 37 is not divisible by 2, we say it is an odd prime number.
b.The factors of 45 are 1, 3, 5, 9, 15, and 45. Since it has factors other than 1 and
45, 45 is notprime. It is an odd composite number.
Self Check 4
a.Is 39 a prime number?
b.Is 57 a prime number?
Now TryProblems 53 and 57
3 Find prime factorizations using a factor tree.
Every composite number can be formed by multiplying a specific combination of
prime numbers. The process of finding that combination is called prime
factorization.