Mah problem, in class no substitute beed

You need the greatest common factor of the two numbers.

First, we find the prime factorization of each number.

72/2 = 36
36/2 = 18
18/2 = 9
9/3 = 3
3/3 = 1

72 = 2^3 * 3^2

90/2 = 45
45/3 = 15
15/3 = 5
5/5 = 1

90 = 2 * 3^2 * 5

To find the GCF, use only common factors with the lower exponent.

Both 72 and 90 have 2 as a factor. 72 has 2^3, and 90 has 2. 2 has a lower exponent than 2^3, so we use 2.

Both 72 and 90 have 3 as a factor. The both have 3^2, so we use 3^2.

90 has 5 as a factor, but 72 does not, so 5 is not a common factor, so we do not use 5.

The GCF is the product of the factor we use.

GCF = 2 * 3^2 = 2 * 9 = 18

The greatest number of students he can place in a row is 18.