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A rectangular piece of paper measure 96 cm by 84 cm.it is cut into square piece of equal length such that no paper is wasted. what is the maximum length of a square piece?

answer with calculations please

User Dimbslmh
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To find the maximum length of a square piece that can be cut from a rectangular piece of paper without any wastage, we need to determine the greatest common divisor (GCD) of the two dimensions of the rectangle (96 cm and 84 cm).

The GCD will represent the side length of the largest square that can be evenly divided from both dimensions.

Using the Euclidean algorithm, we can find the GCD as follows:

Step 1: Divide the larger number (96 cm) by the smaller number (84 cm).

96 ÷ 84 = 1 remainder 12

Step 2: Replace the larger number with the remainder obtained (84 cm) and divide the previous remainder (12 cm) by the new number.

84 ÷ 12 = 7 remainder 0

Step 3: Since the remainder is 0, we stop here.

The GCD is the last non-zero remainder obtained, which is 12 cm.

Therefore, the maximum length of a square piece that can be cut from the rectangular paper without wastage is 12 cm.

User Herard
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