Debbie has two pieces of rope one 20ft.long the other 14ft. 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 ft. That she can make?
What is the greatest common factor of 14 and 20?
To find the greatest length in feet that Debbie can make by cutting the two ropes into equal-length pieces without any leftover, we need to find the greatest common divisor (GCD) of the two given rope lengths.
The GCD refers to the largest number that evenly divides both numbers without leaving a remainder. In this scenario, the GCD will represent the length of the largest possible equal pieces of rope.
To find the GCD of 20ft and 14ft, we can use the Euclidean algorithm, which involves dividing the larger number by the smaller number and then taking the remainder. This process is repeated until we obtain a remainder of 0.
Let's calculate the GCD:
Step 1: Divide 20ft by 14ft. The remainder is 6ft.
Step 2: Divide 14ft by 6ft. The remainder is 2ft.
Step 3: Divide 6ft by 2ft. The remainder is 0.
Since we have obtained a remainder of 0, we can conclude that the GCD of 20ft and 14ft is 2ft.
Therefore, the greatest length Debbie can make by cutting the ropes is 2ft.