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Linda has two pieces of cord, one 25 feet long and the other 30 feet long. She wants to cut them up to produce many pieces of cord that are all of the same length, with no cord left over. What is the greatest length, in feet, that she can make them?

Question

Linda has two pieces of cord, one 25 feet long and the other 30 feet long. She wants to cut them up to produce many pieces of cord that are all of the same length, with no cord left over. What is the greatest length, in feet, 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 pieces of cord. 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 25 and 30:

  1. List the prime factors of each number:

    • The prime factors of 25 are 5 and 5.
    • The prime factors of 30 are 2, 3, and 5.

  2. Identify the common prime factors:

    • The common prime factor is 5.

  3. Multiply the common prime factors:

    • 5

So, the greatest length that Linda can cut the cords into, without any leftover, is 5 feet.

This problem has been solved

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