The factors of 20 are [1, 2, 4, 5, 10, 20] and the factors of 52 are [1, 2, 4, 13, 26, 52]. They share 3 factors [1, 2, 4] making 4 the greatest factor 20 and 52 have in common.

There are 2 2-passenger taxis available so that's 2 x 2 = 4 total seats. There are 8 people needing transportation leaving 8 - 4 = 4 who will have to find other transportation.

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{z^6}{9z^3} \)
\( \frac{1}{9} \) z^{(6 - 3)}
\(\frac{1}{9}\)z³

21% of the water consumption is industrial use and 11% is personal use so (21% - 11%) = 10% more water is used for industrial purposes. 10,000 gallons are consumed daily so industry consumes \( \frac{10}{100} \) x 10,000 gallons = 1,000 gallons.