The greatest integer n for which 6^n divides (33)! ,

Answers (1)

Solution:    E_2  =  The exponent of 2 in (33)!

                      E_2=[frac332]+[frac332^2]+[frac332^3]+[frac332^4]+[frac332^5]

                    E_2=16+8+4+2+1=31.

                   E_3 = The exponent of 3 in (33)!

                  E_3=[frac333]+[frac333^2]+[frac333^3]=11+3+1=15.

              We can write    (33)!=k	imes 2^31	imes 3^15,

             	herefore     6^n  divides    (33)!  for   n=15.

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