The number of zeros at the end of 100 ! is

Answers (1)

Solution:      E_2(100!) = The exponent of 2 in (100!)

                       E_2(100!)=[frac1002]+[frac1002^2]+[frac1002^3]+[frac1002^4]+[frac1002^5]+[frac1002^6]

                       E_2(100!)=50+25+12+6+3+1=97.          

                       E_5(100!)=[frac1005]+[frac1005^2]=20+4=24.

                      E_10(100!)=Min97,24=24.               

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