In order for the students to be arranged in a rectangular grid with no gaps, the number of students must form a rectangle. A rectangle has two dimensions, so the number of students must be a product of two numbers.
The factors of a number can be found by using prime factorization. Let's prime factorize the numbers 10 and 15:
10 = 2 x 5
15 = 3 x 5
Since a rectangle can only have one straight line of desks, the number of students must be the product of the maximum and minimum factors of the number.
The largest number of students that Jon could have in his class is 2 x 5 x 3 = 30.
Jon teaches a fourth grade class at an elementary school where class sizes are always at least 10 students and at most 15. 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. What is the largest number of students that Jon could have in his class?
1 answer
1 answer