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What is the maximum length of piece of ribbon if two long piece of ribbon ,800cm and 640cm long are cut into equal piece.how many such small piece of ribbon will be there?

Sagot :

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Answer:

To determine the maximum length of each piece of ribbon and how many such pieces can be cut from the two given lengths of ribbon, we need to find the greatest common divisor (GCD) of 800 cm and 640 cm. The GCD will be the maximum length of each equal piece.

Here's the step-by-step process:

1. Find the GCD of 800 and 640:

- List the factors of each number:

- Factors of 800: 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800

- Factors of 640: 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 320, 640

- Identify the common factors:

- Common factors: 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160

- The greatest common factor is 160.

2. Calculate the number of pieces:

- For the 800 cm ribbon:

- Number of pieces = Total length / Length of each piece

- Number of pieces = 800 cm / 160 cm = 5 pieces

- For the 640 cm ribbon:

- Number of pieces = Total length / Length of each piece

- Number of pieces = 640 cm / 160 cm = 4 pieces

Thus, the maximum length of each piece of ribbon is 160 cm, and there will be a total of 5 + 4 = 9 pieces.

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