What is the largest prime factor of 8 × 7 × 6 × 5 × 4 × 3 − 6 × 5 × 4 × 3 × 2 × 1?

2. Let the length of the rectangle be x cm and the width = (x - 4) cm. Area = x(x - 4) = (x^2 - 4x) cm^2

If the length and the width are both decreased by 2cm, new length = (x - 2) cm and new width = (x - 4 - 2) = (x - 6) cm. New area = (x - 2)(x - 6) = (x^2 - 8x + 12) cm^2

Original area - 24cm^2 = new area

x^2 - 4x - 24 = x^2 - 8x + 12

-4x + 8x = 12 + 24

4x = 36

x = 36/4 = 9cm

Therefore the original length of the rectangle = 9cm while the original width is 9 - 4 = 5 cm.