Knowee
Questions
Features
Study Tools

Vijay has two pieces of wire, one 18 feet long and the other 12 feet long. If he wants to cut them up to produce many pieces of wire that are all of the same length, with no wire left over, what is the greatest length, in feet, that he can make them?

Question

Vijay has two pieces of wire, one 18 feet long and the other 12 feet long. If he wants to cut them up to produce many pieces of wire that are all of the same length, with no wire left over, what is the greatest length, in feet, that he can make them?

🧐 Not the exact question you are looking for?Go ask a question

Solution

To solve this problem, we need to find the greatest common divisor (GCD) of the lengths of the two wires. 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 18 and 12:

  1. List the prime factors of each number:

    • The prime factors of 18 are 2, 3, 3.
    • The prime factors of 12 are 2, 2, 3.

  2. Identify the common prime factors:

    • The common prime factors are 2 and 3.

  3. Multiply the common prime factors together:

    • 2 * 3 = 6.

So, the greatest length that Vijay can cut the wires into, without any wire left over, is 6 feet.

This problem has been solved

Similar Questions

Omar has two pieces of cord, one 16 feet long and the other 18 feet long. He 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 he can make them?

Seth has two pieces of cable, one 50 feet long and the other 25 feet long. For a science project, he wants to cut them up to produce many pieces of cable that are all of the same length, with no cable left over. What is the greatest length, in feet, that he can make them?

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?

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?

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.

1/3

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.