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Anita has two pieces of string, one 14 feet long and the other 28 feet long. For an art project, she wants to cut them up to produce many pieces of string that are all of the same length, with no string left over. What is the greatest length, in feet, that she can make them?

Question

Anita has two pieces of string, one 14 feet long and the other 28 feet long. For an art project, she wants to cut them up to produce many pieces of string that are all of the same length, with no string 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 two lengths of string, 14 feet and 28 feet. The GCD is the largest number that divides 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 14 are 2 and 7.
    • The prime factors of 28 are 2, 2, and 7.

  2. Identify the common prime factors:

    • The common prime factors are 2 and 7.

  3. Multiply the common prime factors together:

    • 2 * 7 = 14.

So, the greatest length that Anita can cut the strings into, without any leftover, is 14 feet.

This problem has been solved

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