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3.5.2 Exercises

Using the rule a = a·c for any nonzero c, write four fractions equivalent to each given fraction:
b b·c
1
1.
4
3
2.
4
1
3.
5

2
4.
5
1
5.
8
5
6.
8
Using cancellation, reduce each fraction to lowest terms. Convert improper fractions to mixed numbers.

12
7.
8
12
8.
18
20
9.
45
84
10.
60

54
11.
108
360
12.
120

3.6 Prime Factorization and the GCF

Reducing a fraction to lowest terms requires recognizing a common factor (greater than 1) of the
numerator and denominator. Doing it in one step requires finding and using the largest or greatest
common factor. In this section, we develop a systematic way of finding the greatest common factor
(GCF) of a set of numbers.
A whole number greater than 1 is prime if it has no factors other than itself and 1. The first few
prime numbers are
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, ... .

The dots indicate that there are infinitely many larger primes. (This fact is not obvious but was proved
more than two thousand years ago by Euclid.) The whole numbers greater than 1 which are not prime

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