Question

module 2, lesson 2: divisibility by 6. make a conjecture about the rule for each diagram. numbers inside the circle follow the rule. numbers outside the circle do not follow the rule. diagram d: (inside the circle = 400, 30, 2, 432) (outside the circle = 15,105) - is 352 divisible by 3? explain how you know. (with mr. bell) answer: no. the sum of the digits of 352 is 10 because 3 + 5 + 2 = 10. because 10 is not divisible by 3, 352 is also not divisible by 3. - is 192 divisible by 6? explain how you know.

Explanation:

Step1: Recall divisibility rule for 3

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

Step2: Check divisibility of 352 by 3

For 352, sum of digits: $3 + 5+2=10$. Since 10 is not divisible by 3, 352 is not divisible by 3.

Step3: Recall divisibility rule for 6

A number is divisible by 6 if it is divisible by both 2 and 3.

Step4: Check divisibility of 192 by 6

For 192, sum of digits: $1 + 9+2 = 12$. Since 12 is divisible by 3, and 192 is even (ends with 2, so divisible by 2), 192 is divisible by 6.

Answer:

352 is not divisible by 3. 192 is divisible by 6.