Final answer:
To find the greatest number of students per row, we determine the greatest common divisor (GCD) of 18 and 27, which is 9. Thus, the greatest number of students that can stand in each row is 9.
Step-by-step explanation:
The question asks for the greatest number of students that can stand in each row for a choir group consisting of 18 boys and 27 girls where only boys or girls will be in each row. To determine this number, we need to find the greatest common divisor (GCD) of 18 and 27, which is the largest number that can divide both numbers without leaving a remainder.
By listing the factors of 18 (1, 2, 3, 6, 9, 18) and the factors of 27 (1, 3, 9, 27), we can see that the GCD is 9. Therefore, the greatest number of students that can stand in each row is 9.