To determine the greatest possible width of each piece such that they are all the same width for the strips of cloth with widths 72 cm, 96 cm, and 128 cm, we need to find the greatest common divisor (GCD) of these three numbers.
Let's calculate the GCD step by step:
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Factors of 72:
- 72 = 2 × 2 × 2 × 3 × 3 = \(2^3 \times 3^2\)
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Factors of 96:
- 96 = 2 × 2 × 2 × 2 × 3 = \(2^4 \times 3^1\)
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Factors of 128:
- 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2 = \(2^7\)
Now, take the minimum power of each prime factor:
- For the factor 2: the minimum power is \(2^3\) (from 72).
- For the factor 3: the minimum power is \(3^0\) (as 128 does not include factor 3).
Now multiply these together to get the GCD:
\[ GCD = 2^3 \times 3^0 = 8 \]
So, the greatest possible width of each piece so that they are all the same width is 8 cm.
Thus, the correct response is 8 cm.
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