Basic College Mathematics (9th Edition)

Published by Pearson
ISBN 10: 0321825535
ISBN 13: 978-0-32182-553-7

Chapter 2 - Multiplying and Dividing Fractions - 2.3 Factors - 2.3 Exercises: 54

Answer

All primes except 2 must be odd (otherwise they would be divisible by 2). Some odd numbers are not prime (e.g. 15).

Work Step by Step

Prime numbers are defined as (a) whole and (b) only divisible (evenly) by themselves and 1. For example, the numbers $3$, $5$, and $7$ are prime because they have no factor aside from themselves and 1. It is true that all prime numbers are odd, except for 2. This is because any even number would be divisible by itself, 1, and the number 2 (and hence would not be prime). But it does not follow that odd numbers are prime. This is because two prime numbers can multiply to an odd number that is then not prime. For example, $3$ and $5$ are prime. However, if you multiply them, you get $15$, which is odd, but not prime (because it is divisible by $15$, $1$, $3$, and $5$).
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.