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: 47

Answer

$2^{2}\times3^{2}\times5$

Work Step by Step

In order to find the prime factorization of 180, we can try to divide 135 by the first prime, 2. $180\div2=90$ Try to divide 90 by 2. $90\div2=45$ 45 cannot be divided by 2, so we divide by the next prime, 3. $45\div3=15$ 15 cannot be divided by 2, so we divide by 3. $15\div3=5$ 5 itself is a prime number, so we cannot simplify any more. The prime factorization of 135 is $2\times2\times3\times3\times5=2^{2}\times3^{2}\times5$.
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