Question

mr. danville teaches three drama classes.

• the first class has 24 students.
• the second class has 30 students.
• the third class has 18 students.

mr. danville wants to divide each class into groups so that every group in every class has the same number of students and there are no students left over.
what is the maximum number of students that he can put into each group?
a. 8
b. 6
c. 4
d. 2

Explanation:

Step1: Identify the problem type

We need to find the greatest common divisor (GCD) of the number of students in each class: 24, 30, and 18.

Step2: Prime factorize each number

• Prime factorization of 24: $24 = 2^3 \times 3$
• Prime factorization of 30: $30 = 2 \times 3 \times 5$
• Prime factorization of 18: $18 = 2 \times 3^2$

Step3: Find the common prime factors

The common prime factors are 2 and 3.

Step4: Calculate the GCD

Take the lowest power of each common prime factor:

• For 2: the lowest power is $2^1$
• For 3: the lowest power is $3^1$

Multiply these together: $2^1 \times 3^1 = 6$

Answer:

B. 6