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