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A teacher has 48 pencils and 60 erasers. What is the largest number of students

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Question: A teacher has 48 pencils and 60 erasers. What is the largest number of students that can receive the same number of pencils and erasers? (2023)

Options:

  1. 6
  2. 12
  3. 8
  4. 10

Correct Answer: 12

Exam Year: 2023

Solution: 

The HCF of 48 and 60 is 12. Therefore, the largest number of students is 12.

A teacher has 48 pencils and 60 erasers. What is the largest number of students

Practice Questions

Q1
A teacher has 48 pencils and 60 erasers. What is the largest number of students that can receive the same number of pencils and erasers? (2023)
  1. 6
  2. 12
  3. 8
  4. 10

Questions & Step-by-Step Solutions

A teacher has 48 pencils and 60 erasers. What is the largest number of students that can receive the same number of pencils and erasers? (2023)
  • Step 1: Identify the total number of pencils, which is 48.
  • Step 2: Identify the total number of erasers, which is 60.
  • 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 48 and 60.
  • Step 4: List the factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
  • Step 5: List the factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
  • Step 6: Identify the common factors from both lists: 1, 2, 3, 4, 6, 12.
  • Step 7: The largest common factor is 12.
  • Step 8: Therefore, the largest 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 is used to determine how many students can receive equal amounts of items.
  • 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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