What the whole exercise meant to show was application of modulo in other situations creatively. In the specific question the number of children is unknown and don’t try to figure out how many total children are there as it is unnecessary to understanding the lesson.

Let us assume there were 16 children ( don’t mind the number it is just for explanation and not the actual figure) and write down numbers 1 to 16 on a piece of paper. Remember the aim of the exercise is to establish what team out of the 4 a child is to be placed, not how many are in a team. Since there are only 4 teams, the divisor we use is 4. If you follow on a piece of paper you will understand that the first 4 children, denoted by numbers 1,2,3 and 4 will be in the corresponding teams(i.e Team 1, Team 2, Team 3 and Team 4). Now proceed to place child number 5 in Team 1, child number 6 in Team 2, child number 7 in Team 3, and child number 8 in Team 4. Do this for all the 16 numbers (children). If you were to use modulo here, the remainder is:

Child 5 = 1

Child 6 = 2

Child 7 = 3

Child 8 = 0

Child 9 = 1

Child 10 = 2

Child 11 = 3

Child 12 = 0

Child 13 = 1

Child 14 = 2

Child 15 = 3

Child 16 = 0

The modulo answer/remainder corresponds to the Team the child is allocated. Note, that all the numbers divisible by the divisor in our case 4 result in 0. So a return of 0 means the child is allocated in the last group usually the divisor, team number 4.

Therefore in relation to the exercise, you are the 27th child out of an unknown number of children. 27%4 results in 3( the remainder) which is the team you are in. This is not your number on the team or how many out of the team, but just the team you are in. If you use the pen and paper method, you will see the logic.Therefore you cannot accurately deduce how many total children they are, but by knowing the number a child is allocated you will know which team he/she is allocated.

It also answers the question that result of a modulo operation can never be larger than the divisor. It’ll always end up being one less the value of the modulo and then becomes 0 if 1 is added to the number being divided.

Hope this helps someone.

B.S