To solve this problem, we need to find the greatest common divisor (GCD) of the two lengths of string, 43 feet and 86 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 43 are 43 (since 43 is a prime number).
- The prime factors of 86 are 2 and 43 (since 86 = 2 * 43).

2. Identify the common prime factors.
- The common prime factor of 43 and 86 is 43.

3. The GCD is the product of the common prime factors.
- Since the only common prime factor is 43, the GCD is 43.

So, the greatest length, in feet, that Ariana can make the pieces of string is 43 feet.

Question

To solve this problem, we need to find the greatest common divisor (GCD) of the two lengths of string, 43 feet and 86 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 43 are 43 (since 43 is a prime number).
   - The prime factors of 86 are 2 and 43 (since 86 = 2 * 43).

2. Identify the common prime factors.
   - The common prime factor of 43 and 86 is 43.

3. The GCD is the product of the common prime factors.
   - Since the only common prime factor is 43, the GCD is 43.

So, the greatest length, in feet, that Ariana can make the pieces of string is 43 feet.

Knowee AI · Accepted Answer

To solve this problem, we need to find the greatest common divisor (GCD) of the two lengths of string, 43 feet and 86 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 43 are 43 (since 43 is a prime number).
   - The prime factors of 86 are 2 and 43 (since 86 = 2 * 43).

2. Identify the common prime factors.
   - The common prime factor of 43 and 86 is 43.

3. The GCD is the product of the common prime factors.
   - Since the only common prime factor is 43, the GCD is 43.

So, the greatest length, in feet, that Ariana can make the pieces of string is 43 feet.

Ariana has two pieces of string, one 43 feet long and the other 86 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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