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# help

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Jon teaches a fourth grade class at an elementary school where class sizes are always at least 20 students and at most 28. One day Jon decides that he wants to arrange the students in their desks in a rectangular grid with no gaps. Unfortunately for Jon he discovers that doing so could only result in one straight line of desks. How many students does Jon have in his class?

Jun 10, 2018

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In this case, we are getting a 1*x rectangle of desks, and this is the only possible arrangement. This means that x is a prime number. Since his classes can't have less than 20 and more than 28, that means we're looking for a prime number between 20 and 28. Let's run through each number and its factors.

20: 1,2,4,5,10,20

21: 1,3,7,21

22: 1,2,11,22

23: 1,23

24: 1,2,3,4,6,8,12,24

25: 1,5,25

26: 1,2,13,26

27: 1,3,9,27

28: 1,2,4,7,14,28

I might've misses some factors, but that's fine. All that matters is that 23 only has the factors of itself and 1, making it prime. Therefore, Jon has 23 students in his class.

Jun 10, 2018