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Mary has two pieces of ribbon, one 8 inches long and the other 14 inches long. To decorate an album, she wants to cut them up to produce many pieces of ribbon that are all of the same length, with no ribbon left over. What is the greatest length, in inches, that she can make them?

Question

Mary has two pieces of ribbon, one 8 inches long and the other 14 inches long. To decorate an album, she wants to cut them up to produce many pieces of ribbon that are all of the same length, with no ribbon left over. What is the greatest length, in inches, that she can make them?

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Solution

To solve this problem, we need to find the greatest common divisor (GCD) of the lengths of the two ribbons. The GCD of two numbers is the largest number that divides both of them without leaving a remainder.

Here are the steps to find the GCD of 8 and 14:

  1. List the prime factors of each number:

    • The prime factors of 8 are 2, 2, and 2.
    • The prime factors of 14 are 2 and 7.

  2. Identify the common prime factors:

    • The common prime factor is 2.

  3. Multiply the common prime factors:

    • 2

So, the greatest length that Mary can cut the ribbons is 2 inches.

This problem has been solved

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