Between 20 and 28 students signed up for the chess club. The students could not be divided exactly into groups of 2, 3, 4, or 5. How many students signed up for the chess club?

4 answers

2 divides 20,22,24,26,28
3 divides 21,24,27
4 divides 20,24,28
5 divides 20,25
So, which number has not been listed above?
So our number should not be divisible by 2,3,4,or 5
that is, it can't be a multiple of of these numbers

So for the range of 20 - 28
multiples of 2: 20, 22, 24, 26, 28
multiples of 2: 21, 24, 27
multiples of 4: 20, 24, 28
multiples of 5: 20, 25

I don't see the prime number 29, so that's it
Factor all numbers between 20 and 28.

20 = 2² ∙ 5

21 = 3 ∙ 7

22 = 2 ∙ 11

23 is a prime number

24 = 2³ ∙ 3

25 = 5²

26 = 2 ∙ 13

27 = 3³

28 = 2³ ∙ 7

The number 23 is the only number that can't be divided by 2, 3, 4, or 5.

23 students signed up for the chess club
good grief, how did I mess this one up, 29 is not even in the given range.

go with oobleck and bosnian,
it is obviously 23