Kiera has two pieces of rope, one 120 inches long and the other 64 inches long. For a project, she needs to cut them up to produce many pieces of rope that are all of the same length, with no rope left over. What is the greatest length, in inches, that she can make them?
GCD(64,120) = 8
so she can cut them up into 8" pieces, but no longer.
To find the greatest length that Kiera can make the rope pieces, we need to determine the greatest common divisor (GCD) of the two rope lengths. The GCD represents the largest length that can evenly divide both numbers without any remainder.
To find the GCD, we can use the Euclidean algorithm. Here's how:
1. Start by dividing the larger rope length (120 inches) by the smaller rope length (64 inches). The remainder of this division is calculated as 120 % 64 = 56.
2. Now, divide the smaller rope length (64 inches) by the remainder obtained from the previous step (56 inches). The new remainder is calculated as 64 % 56 = 8.
3. Repeat this process until the remainder becomes zero. In this case, we divide 56 inches by 8 inches, resulting in a remainder of 0.
4. The last non-zero remainder obtained in the previous step (8 inches) is the GCD of the two rope lengths.
Therefore, the greatest length that Kiera can make the rope pieces is 8 inches.