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A teacher has 36 pencils and 48 erasers. What is the maximum number of students

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Question: A teacher has 36 pencils and 48 erasers. What is the maximum number of students that can receive the same number of pencils and erasers? (2023)

Options:

  1. 6
  2. 12
  3. 18
  4. 24

Correct Answer: 12

Exam Year: 2023

Solution: 

The maximum number of students is the HCF of 36 and 48, which is 12.

A teacher has 36 pencils and 48 erasers. What is the maximum number of students

Practice Questions

Q1
A teacher has 36 pencils and 48 erasers. What is the maximum number of students that can receive the same number of pencils and erasers? (2023)
  1. 6
  2. 12
  3. 18
  4. 24

Questions & Step-by-Step Solutions

A teacher has 36 pencils and 48 erasers. What is the maximum number of students that can receive the same number of pencils and erasers? (2023)
  • Step 1: Identify the total number of pencils, which is 36.
  • Step 2: Identify the total number of erasers, which is 48.
  • Step 3: To find out how many students can receive the same number of pencils and erasers, we need to find the highest common factor (HCF) of 36 and 48.
  • Step 4: List the factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.
  • Step 5: List the factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
  • Step 6: Identify the common factors from both lists: 1, 2, 3, 4, 6, 12.
  • Step 7: The highest common factor (HCF) is the largest number in the common factors list, which is 12.
  • Step 8: Therefore, the maximum number of students that can receive the same number of pencils and erasers is 12.
  • Highest Common Factor (HCF) – The HCF is the largest number that divides two or more numbers without leaving a remainder, which in this case helps determine how many students can receive equal amounts of pencils and erasers.
  • Division of Resources – Understanding how to evenly distribute resources (pencils and erasers) among a group of individuals (students) based on the HCF.
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