A teacher is making back to school supply gifts for his students. He has 72 pencils and 96 erasers. If he is giving each student the same number of pencils and the same number of erasers, how many students are in his class? He will have no extra bags after he distributes them.(1 point)

Question

There must be
students in his class

Answer 1

To find out how many students are in the class, we need to determine the greatest common divisor (GCD) of the number of pencils (72) and the number of erasers (96). The GCD will give us the largest number of students such that each student receives the same number of pencils and erasers with none left over.

Let's calculate the GCD of 72 and 96.

Step 1: Prime Factorization

• The prime factorization of 72:
  • \( 72 = 2^3 \times 3^2 \)
• The prime factorization of 96:
  • \( 96 = 2^5 \times 3^1 \)

Step 2: Identify the lowest powers of shared prime factors

• The common prime factors are \(2\) and \(3\):
  • For \(2\): the lowest power is \(2^3\)
  • For \(3\): the lowest power is \(3^1\)

Step 3: Calculate the GCD \[ \text{GCD} = 2^3 \times 3^1 = 8 \times 3 = 24 \]

Thus, the GCD of 72 and 96 is 24, which means that the teacher can evenly distribute the supplies to 24 students.

Therefore, there must be 24 students in his class.