Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 5 - Number Theory and the Real Number System - Chapter 5 Test - Page 337: 1

Answer

\[2,\,\,3,\,\,4,\,\,6,\,\,8,\,\,9\,\,and\,\,12\].

Work Step by Step

Write 391248 in terms of prime factors as follows: \[391,248=2\times 2\times 2\times 2\times 3\times 3\times 11\times 13\times 19\] Now, check which of the provided numbers can be obtained by multiplying the prime factors of \[391,248\] as follows: \[\begin{align} & 2=2 \\ & 3=3 \\ & 4=2\times 2 \\ & 5=\text{cannot be obtained} \\ \end{align}\] \[\begin{align} & 6=2\times 3 \\ & 8=2\times 2\times 2 \\ \end{align}\] \[\begin{align} & 9=3\times 3 \\ & 10=2\times 5\left( \text{cannot be obtained} \right) \\ & 12=2\times 2\times 3 \\ \end{align}\] So, the numbers that can divide 391248 are\[2,\,\,3,\,\,4,\,\,6,\,\,8,\,\,9\,\,and\,\,12\].
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