Question
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)
There must be
students in his class.
To find the number of students in the class, we need to find the greatest common divisor (GCD) of 72 and 96. The GCD represents the largest number that both 72 and 96 can be divided evenly by.
Prime factorization of 72: 2^3 * 3^2
Prime factorization of 96: 2^5 * 3
To find the common factors, we take the smallest exponent for each prime factor:
Common factors: 2^3 * 3 = 24
Therefore, there are 24 students in the class.