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Super rare math problem
The common factor of 105 and 70 is 1, 5, 7, 35.

So there are four different incisions.

The side length of (1) square is 1 cm, and it can be cut (105 ÷1) × (70 ÷1) = 7350.

(2) The side length of a square is 5cm, and it can be cut into (105 ÷ 5) × (70 ÷ 5) = 294 pieces.

(3) A square with a side length of 7 cm can be cut into (105 ÷ 7) × (70 ÷ 7) =150 pieces.

(4) The side length of a square is 35cm, which can be cut by (105 ÷ 35) × (70 ÷ 35) = 5.