What is the largest prime factor of (25!)^3 - (24!)^3 ?

1 Answer
Jul 31, 2015

31

Explanation:

(25!)^3-(24!)^3 = (25*24!)^3-(24!)^3 = 25^3(24!)^3-(24!)^3

=(25^3-1)(24!)^3 = (15625-1)(24!)^3 = 15624(24!)^3

15624 = 2^3*3^2*7*31

The largest prime factor of (24!)^3 is the largest prime factor of 24! which is 23