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A teacher is making back to school supply gifts for his students. He has 72 pencils and 96 erasers. If he is giving each studen...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.
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GPT 3.5
To find the number of students in the class, we need to determine the greatest common divisor (GCD) of the number of pencils and erasers. The GCD will represent the number of students, as it represents the largest number that evenly divides both the number of pencils and erasers.
The prime factorization of 72 is: 2^3 * 3^2
The prime factorization of 96 is: 2^5 * 3
To find the GCD, we take the minimum exponent for each prime factor:
- 2 (minimum exponent of 2 in 72 and 96)
- 3 (minimum exponent of 3 in 72 and 96)
Thus, the GCD of 72 and 96 is 2^2 * 3 = 12.
Therefore, there are 12 students in the class.
The prime factorization of 72 is: 2^3 * 3^2
The prime factorization of 96 is: 2^5 * 3
To find the GCD, we take the minimum exponent for each prime factor:
- 2 (minimum exponent of 2 in 72 and 96)
- 3 (minimum exponent of 3 in 72 and 96)
Thus, the GCD of 72 and 96 is 2^2 * 3 = 12.
Therefore, there are 12 students in the class.
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