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There are two cables. Cable X is 24 m long. Cable Y is 36 m long.Sarah wants to cut the cables into pieces of equal length with no leftovers.Find the greatest length of each piece of cable she can cut.

Question

There are two cables. Cable X is 24 m long. Cable Y is 36 m long.Sarah wants to cut the cables into pieces of equal length with no leftovers.Find the greatest length of each piece of cable she can cut.

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Solution

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

Here are the steps:

  1. List the prime factors of each number:

    • Prime factors of 24 are 2, 2, 2, 3
    • Prime factors of 36 are 2, 2, 3, 3

  2. Identify the common prime factors: 2, 2, 3

  3. Multiply these common prime factors together: 2 * 2 * 3 = 12

So, the greatest length of each piece of cable Sarah can cut is 12 meters.

This problem has been solved

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