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?

Given:

Miyu has 36 grapes.

Determine the size group of friends which makes it impossible for Miyu to share her grapes equally.

Solution:

Since we are asked to find the group of friends in which Miyu cannot share her grapes equally, we will first determine the group of friends where Miyu can share her grapes equally. In order to do so, we determine the factors of 36.

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Miyu can share her 36 grapes to the following group sizes; 2 with 18 grapes each, 3 with 12 grapes each, 4 with 9 grapes each, 6 with 6 grapes each, 9 with 4 grapes each, 12 with 3 grapes each, and 18 with 2 grapes each.

Since there is no limitation on the number of friends that Miyu cannot share her grapes equally, therefore we can conclude that Miyu cannot share her grapes equally from a group of 5, 7, 8, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, and 35 friends.