Walter has two pieces of cable, one 16 feet long and the other 12 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? _____ feet

Question

Walter has two pieces of cable, one 16 feet long and the other 12 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?  _____ feet

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Identify Problem:  Identify the problem: Walter needs to cut his cables into pieces of equal length with no leftovers. We need to find the greatest length that works for both cables. Find GCD:  Find the greatest common divisor (GCD) of the lengths of the two cables. The lengths are 16 feet and 12 feet. List Divisors:  List the divisors of 16: 1, 2, 4, 8, 16. List the divisors of 12: 1, 2, 3, 4, 6, 12. The common divisors are 1, 2, 4. The greatest common divisor is 4. Calculate Length:  Calculate the greatest length for the cable pieces: The GCD of 16 and 12 is 4 feet, so Walter can cut the cables into pieces that are each 4 feet long.

Walter has two pieces of cable, one $16$ feet long and the other $12$ 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? $\newline$ _____ feet

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