Question

Jazmyn has some strips of cloth she found for her project. The widths of the different strips are 72 cm, 96 cm, and 128 cm. They are to be cut into smaller pieces. Determine the greatest possible width of each piece so that they are all the same width.(1 point)

Answer 1

To find the greatest possible width of each piece that Jazmyn can cut from the strips of cloth so that they all have the same width, we need to determine the greatest common divisor (GCD) of the widths of the strips. The GCD of 72 cm, 96 cm, and 128 cm will give us the largest width that can be used to cut each strip without any remainder.

Here's how you would calculate the GCD:

1. List the factors of each number, or use a more systematic method such as the Euclidean algorithm.
2. Find the largest factor that is common to all three numbers.

Since the Euclidean algorithm is efficient for large numbers, let's use that approach:

First, find the GCD of 72 and 96:
96 = 72 × 1 + 24
72 = 24 × 3 + 0

The remainder is 0, which means that the GCD of 72 and 96 is 24.

Now that we have the GCD of the first two numbers, we will find the GCD of this result (24) with the third number (128):

128 = 24 × 5 + 8
24 = 8 × 3 + 0

The remainder is 0, which means that the GCD of 24 and 128 is 8.

Thus, the GCD of 72, 96, and 128 is 8 cm. So Jazmyn can cut the strips into smaller pieces that are each 8 cm wide, and there will be no waste leftover from any of the strips.