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

Sagot :

LammettHash

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

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