larlialaurier larlialaurier

15-08-2021
Mathematics

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Find the largest prime factor of 18! + 19! + 20!

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LammettHash LammettHash

18-08-2021

18! is common to each term in the sum:

18! + 19! + 20! = 18! (1 + 19 + 19×20) = 18!×400

The largest prime factor of 18! is of course 17.

Meanwhile,

400 = 16×25 = 2⁴×5²

so the largest prime factor of 18! + 19! + 20! is 17.

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