Question

answer the questions below. be sure to mark all answers that apply.

	465	882	163	none of these
(b) which numbers are divisible by 3?	□	□	□	□

Explanation:

Step1: Recall divisibility rules

A number is divisible by 9 if the sum of its digits is divisible by 9, and divisible by 3 if the sum of its digits is divisible by 3.

Step2: Calculate digit - sum for 465

The sum of digits of 465 is \(4 + 6+5=15\). Since \(15\div3 = 5\) and \(15\div9=1\cdots\cdots6\), 465 is divisible by 3 but not by 9.

Step3: Calculate digit - sum for 882

The sum of digits of 882 is \(8 + 8+2 = 18\). Since \(18\div3=6\) and \(18\div9 = 2\), 882 is divisible by both 3 and 9.

Step4: Calculate digit - sum for 163

The sum of digits of 163 is \(1+6 + 3=10\). Since \(10\div3=3\cdots\cdots1\) and \(10\div9 = 1\cdots\cdots1\), 163 is not divisible by 3 or 9.

Answer:

(a) 882
(b) 465, 882