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Camille has 63 packets of sugar and 84 packets of artificial sweetener. She wants to divide them into identical groups, with no packets left over, so that the groups can be distributed to some tables at the restaurant where she works. What is the greatest number of groups Camille can make?

Question

Camille has 63 packets of sugar and 84 packets of artificial sweetener. She wants to divide them into identical groups, with no packets left over, so that the groups can be distributed to some tables at the restaurant where she works. What is the greatest number of groups Camille can make?

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Solution

To solve this problem, we need to find the greatest common divisor (GCD) of 63 and 84. The GCD is the largest number that can divide both numbers without leaving a remainder.

Here are the steps to find the GCD:

  1. First, list the prime factors of each number.

    • The prime factors of 63 are 3, 3, and 7.
    • The prime factors of 84 are 2, 2, 3, and 7.

  2. Next, identify the common prime factors.

    • The common prime factors are 3 and 7.

  3. Then, multiply the common prime factors together to find the GCD.

    • 3 * 7 = 21

So, the greatest number of groups Camille can make is 21.

This problem has been solved

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