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Answer :
Final answer:
The greatest length of ribbon Rob can use is 24 inches.
Explanation:
To find the greatest length of ribbon that Rob can use, we need to find the greatest common divisor (GCD) of 48 and 72. The GCD represents the largest length that can be evenly divided into both quantities. In this case, the GCD is 24 inches. Therefore, Rob can cut the ribbons into 24-inch pieces.
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He can cut the purple ribbon into 2 pieces of length 24 inches each (since 2 x 24 = 48), and the green ribbon into 3 pieces of length 24 inches each (since 3 x 24 = 72).
To find the greatest length of ribbon that Rob can use, we need to find the greatest common factor (GCF) of 48 and 72, and then divide both numbers by that factor.
First, we can find the prime factorization of both numbers:
48 = 2 x 2 x 2 x 2 x 3
72 = 2 x 2 x 2 x 3 x 3
Next, we can identify the common factors as 2, 2, 2, and 3, and their product is 2 x 2 x 2 x 3 = 24. Therefore, 24 is the greatest common factor of 48 and 72.
To cut the ribbon into same-length pieces, Rob can use a length of 24 inches, which is the greatest common factor of the original lengths of ribbon. He can cut the purple ribbon into 2 pieces of length 24 inches each (since 2 x 24 = 48), and the green ribbon into 3 pieces of length 24 inches each (since 3 x 24 = 72). This way, he uses up all the ribbon with no leftovers.
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