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 - 5.1 Number Theory: Prime and Composite Numbers - Exercise Set 5.1: 3

Answer

The number 21408 is divisible by: 2, 3, 4, 6, 8, and 12. It is not divisible by: 5, 9, and 10.

Work Step by Step

Using divisibility rules we find that 21408 is divisible by: a. 2 --Yes. It is an even number. b. 3 --yes. The sum of its digits (2 + 1 + 4 + 0 + 8 = 15) is divisible by 3. c. 4 -- yes. The last two digits (08) make a number that is divisible by 4. d. 5 -- No. The ones digit is not a 0, nor is it a 5. e. 6 --yes. It is divisible by both 2 and 3. f. 8 -- yes. The number's last three digits (408) make a number that is divisible by 8. g. 9 --no. The sum of its digits (15) is not divisible by 9. h. 10 -- no. Its ones digit is not a zero. i. 12 --yes. It is divisible by both 3 and 4.
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