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?
Question
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?
Solution
To solve this problem, we need to find the greatest common divisor (GCD) of the two lengths of cable, 50 feet and 25 feet. The GCD is the largest number that divides both numbers without leaving a remainder.
Step 1: List the divisors of each number.
The divisors of 50 are: 1, 2, 5, 10, 25, 50. The divisors of 25 are: 1, 5, 25.
Step 2: Identify the common divisors.
The common divisors are: 1, 5, 25.
Step 3: The greatest common divisor is the largest of these, which is 25.
So, Seth can cut the cables into pieces that are each 25 feet long.
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