A natural number greater than 1 that is not prime is called a composite number.
4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21 First dozen composite numbers
By agreement, the number 1 is neither prime nor composite.
Sometimes we must find all prime factorsof a number—those factors which are
prime numbers.
Factoring NumbersWrite each number as the product of prime factors.
(a) 35
Write 35 as the product of the prime factors 5 and 7, or as
(b) 24
We show a factor tree on the right. The prime factors are circled.
24
Divide by the least prime
factor of 24, which is 2.
Divide 12 by 2 to find two
factors of 12.
Now factor 6 as
All factors are prime. NOW TRY2 #3. 24 = 2 # 2 # 2 # 3 2 # 3
24 = 2 # 2 # 6 2 # 6
24 = 2 # 12 2 # 12
35 = 5 # 7.
EXAMPLE 1
SECTION 1.1 Fractions 3
NOW TRY
EXERCISE 1
Write 60 as the product of
prime factors.
⎧⎪⎪⎨⎪⎪⎩
Basic Principle of FractionsIf the numerator and denominator of a fraction are multiplied or divided by the
same nonzero number, the value of the fraction is not changed.
NOTE When factoring, we need not start with the least prime factor. No matter
which prime factor we start with, we will alwaysobtain the same prime factorization.
Verify this in Example 1(b)by starting with 3 instead of 2.
OBJECTIVE 2 Write fractions in lowest terms.Recall the following basic
principle of fractions,which is used to write a fraction in lowest terms.
A fraction is in lowest termswhen the numerator and denominator have no fac-
tors in common (other than 1).
NOW TRY ANSWER
- 2 # 2 # 3 # 5
Writing a Fraction in Lowest Terms
Step 1 Write the numerator and the denominator as the product of prime
factors.
Step 2 Divide the numerator and the denominator by the greatest common
factor,the product of all factors common to both.