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 out how many students are in the class, we need to find the greatest common divisor (GCD) of 72 and 96.
First, we can simplify both numbers by dividing both by 4:
72 ÷ 4 = 18
96 ÷ 4 = 24
Now, we can find the GCD of 18 and 24:
18 = 2 × 3 × 3
24 = 2 × 2 × 2 × 3
The GCD of 18 and 24 is 2 × 3 = 6.
Therefore, there are 6 students in the teacher's class.
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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 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 determine the maximum number of students that can be evenly distributed with 72 pencils and 96 erasers. In order to do this, we can find the greatest common divisor (GCD) of the two numbers.
To find the GCD, we can use a method such as prime factorization or the Euclidean algorithm. Let's use the Euclidean algorithm, which involves finding the remainder when dividing the larger number by the smaller number and repeating this process until the remainder is 0.
1. Divide 96 by 72: 96 ÷ 72 = 1 remainder 24
2. Divide 72 by 24: 72 ÷ 24 = 3 remainder 0
Since we have reached a remainder of 0, the GCD is the divisor used in the last operation, which is 24.
The GCD represents the largest number of items (pencils and erasers in this case) that can be evenly distributed to the students without any extras. Therefore, the teacher can distribute 24 pencils and 24 erasers to each student.
To find the number of students, we can divide the total number of pencils or erasers by the number of items per student:
Number of students = Total number of pencils ÷ Number of pencils per student
= 72 pencils ÷ 24 pencils per student
= 3 students
Therefore, the teacher has 3 students in his class.