Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 4 - Elementary Number Theory and Methods of Proof - Exercise Set 4.3 - Page 178: 9

Answer

Yes, $4$ is a factor of $2a\times34b$, because $2a\times34b=2a\times(2\times17)b=4(a\times17b)$, where $a\times17b$ is an integer because it is a product of integers.

Work Step by Step

Note that "is a factor of" means the same thing as "divides." Further, recall that $a|b$ for integers $a$ and $b$ with $a\ne0$, if and only if $b=ka$ for some integer $k$. Here, $k=a\times17b$.
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