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

1 Answer
George C.
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#

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