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An event has 24 adults and 42 children. The event planner wants to make each table identical, with the same combination of adults and children and no people left over. What is the greatest number of tables the planner can set up?

Question

An event has 24 adults and 42 children. The event planner wants to make each table identical, with the same combination of adults and children and no people left over. What is the greatest number of tables the planner can set up?

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Solution

To find the greatest number of tables the event planner can set up, we need to determine the largest possible common factor of 24 and 42.

Step 1: Find the prime factors of 24 and 42:

  • The prime factors of 24 are 2, 2, 2, and 3 (2 x 2 x 2 x 3).
  • The prime factors of 42 are 2, 3, and 7 (2 x 3 x 7).

Step 2: Identify the common prime factors:

  • The common prime factors of 24 and 42 are 2 and 3.

Step 3: Determine the greatest common factor (GCF):

  • The GCF of 24 and 42 is the product of the common prime factors, which is 2 x 3 = 6.

Therefore, the greatest number of tables the event planner can set up is 6.

This problem has been solved

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