The factors of 32 are [1, 2, 4, 8, 16, 32] and the factors of 32 are [1, 2, 4, 8, 16, 32]. They share 6 factors [1, 2, 4, 8, 16, 32] making 32 the greatest factor 32 and 32 have in common.

The area of a circle is given by the formula A = πr² where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))². If the diameter of the logo increases by 65% the radius (and, consequently, the total area) increases by \( \frac{65\text{%}}{2} \) = 32\(\frac{1}{2}\)%

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $500
i = 0.05 x $500

No payments were made so the total amount due is the original amount + the accumulated interest:

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{3}{9} \) x \( \frac{3}{9} \) = \( \frac{3 x 3}{9 x 9} \) = \( \frac{9}{81} \) = \(\frac{1}{9}\)

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{9}{9}} \)
\( \frac{\sqrt{9}}{\sqrt{9}} \)
\( \frac{\sqrt{3^2}}{\sqrt{3^2}} \)
1