The factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36] and the factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40]. They share 3 factors [1, 2, 4] making 4 the greatest factor 36 and 40 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 60% the radius (and, consequently, the total area) increases by \( \frac{60\text{%}}{2} \) = 30%

To divide fractions, invert the second fraction and then multiply:

\( \frac{1}{7} \) ÷ \( \frac{1}{9} \) = \( \frac{1}{7} \) x \( \frac{9}{1} \)

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

\( \frac{1}{7} \) x \( \frac{9}{1} \) = \( \frac{1 x 9}{7 x 1} \) = \( \frac{9}{7} \) = 1\(\frac{2}{7}\)

The equation for this sequence is:

a_n = a_n-1 + 3(n - 1)

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 3(6 - 1)
a₆ = 31 + 3(5)
a₆ = 46

A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.