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Ruben wants to create snack bags for a trip he is going on. He has 16 granola bars and 24 pieces of dried fruit. If the snack bags should be identical without any food left over, what is the greatest number of snack bags Ruben can make?

Question

Ruben wants to create snack bags for a trip he is going on. He has 16 granola bars and 24 pieces of dried fruit. If the snack bags should be identical without any food left over, what is the greatest number of snack bags Ruben can make?

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Solution

To solve this problem, we need to find the greatest common divisor (GCD) of the two numbers, 16 and 24. The GCD is the largest number that can divide both numbers without leaving a remainder.

Here are the steps to find the GCD:

  1. List the prime factors of each number:

    • The prime factors of 16 are 2 x 2 x 2 x 2.
    • The prime factors of 24 are 2 x 2 x 2 x 3.

  2. Identify the common prime factors:

    • The common prime factors are 2 x 2 x 2.

  3. Multiply the common prime factors to get the GCD:

    • 2 x 2 x 2 = 8.

So, the greatest number of snack bags Ruben can make is 8.

This problem has been solved

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