Find the Class Size: Dividing Students into Groups of 8, 4, and 2

A teacher divides the students in his class into group discussions.

On the first day he divides them into groups of 8.

On the second day he divides them into pairs.

On the third day, he divides them into groups of 4.

The division is exact and no students are left without a group.

Calculate the number of students in the class, given that the number of students in the class ranges from 29 to 39.

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1

Understand the problem

A teacher divides the students in his class into group discussions.

On the first day he divides them into groups of 8.

On the second day he divides them into pairs.

On the third day, he divides them into groups of 4.

The division is exact and no students are left without a group.

Calculate the number of students in the class, given that the number of students in the class ranges from 29 to 39.

2

Step-by-step solution

To determine the number of students, let's find all multiples of 8 within the given range of 29 to 39.

  • Calculating multiples of 8: 8×1=8 8 \times 1 = 8 , 8×2=16 8 \times 2 = 16 , 8×3=24 8 \times 3 = 24 , 8×4=32 8 \times 4 = 32 , 8×5=40 8 \times 5 = 40 .

The relevant multiple of 8 that falls within the 29 to 39 range is 32 32 .

Thus, the number of students in the class is 32 32 .

This means that on any given day, all students can indeed be grouped as specified without any remainder.

Therefore, the solution to the problem is 32 32 .

3

Final Answer

32 32

Practice Quiz

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Determine if the following number is divisible by 3:

\( 352 \)

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