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Camilla is making stationery sets from 46 sheets of paper and 69 envelopes. If she wants all the sets to be identical without any paper or envelopes left over, what is the greatest number of sets Camilla can make?

Question

Camilla is making stationery sets from 46 sheets of paper and 69 envelopes. If she wants all the sets to be identical without any paper or envelopes left over, what is the greatest number of sets Camilla can make?

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Solution

To find the greatest number of sets Camilla can make, we need to find the greatest common divisor (GCD) of 46 and 69. 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 46 are 2 and 23.
    • The prime factors of 69 are 3 and 23.

  2. Identify the common prime factors.

    • The common prime factor is 23.

  3. The GCD is the product of the common prime factors.

    • So, the GCD of 46 and 69 is 23.

Therefore, the greatest number of sets Camilla can make is 23.

This problem has been solved

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