Question

miyu has 36 grapes to share with her friends. she wants to make sure each friend gets an equal number of grapes. which size group of friends makes it impossible for miyu to share her grapes equally? 3 people 8 people 9 people 12 people

Explanation:

Step1: Check divisibility by 3

To check if 36 is divisible by 3, we use the rule that a number is divisible by 3 if the sum of its digits is divisible by 3. The sum of digits of 36 is \(3 + 6 = 9\), and \(9\div3 = 3\) with no remainder. So, \(36\div3 = 12\), which is an integer.

Step2: Check divisibility by 8

We perform the division \(36\div8\). \(8\times4 = 32\) and \(36 - 32 = 4\). So, \(36\div8 = 4\) with a remainder of 4. This means 36 is not divisible by 8.

Step3: Check divisibility by 9

A number is divisible by 9 if the sum of its digits is divisible by 9. The sum of digits of 36 is \(3+6 = 9\), and \(9\div9 = 1\) with no remainder. So, \(36\div9 = 4\), which is an integer.

Step4: Check divisibility by 12

We perform the division \(36\div12\). \(12\times3 = 36\), so \(36\div12 = 3\), which is an integer.

Answer:

8 people