What is the largest integer k for which 85! is divisible by 42k?

85! = 85 × 84 × 83 × … × 43 × 42 × 41 × … × 3 × 2 × 1

Dividing 85! by 42 removes the factor of 42 in the middle:

85!/42 = 85 × 84 × 83 × … × 43 × 41 × … × 3 × 2 × 1

and the remaining divisor on the right consists of 84 integers whose product is

6,707,390,748,525,119,707,022,570,100,620,503,797,144,205,579,299,385,866,788,140,779,822,857,765,709,426,986,929,530,629,817,641,048,054,169,600,000,000,000,000,000,000

d. it is a convex pentagon because it has five sides and none of the sides would extend into the inside of the polygon.

step-by-step explanation: