Write out 50! in full and delete all of its trailing zeros. The…

Question

Write out 50! in full and delete all of its trailing zeros. The resulting number ends in some two digits. Find that two-digit number (the last two nonzero digits of 50!).

Accepted Answer

50! has v_5 = 10+2 = 12 trailing-zero-producing fives and v_2 = 25+12+6+3+1 = 47 twos, so it ends in exactly 12 zeros. Remove the 12 factors of 10; the remaining number's last two digits are determined by the product of all factors with 12 fives and 12 of the twos cancelled, taken mod 100. Carefully tracking the unit-removed factorial modulo 100 (equivalently mod 4 and mod 25 and combining), the last two nonzero digits come out to 12. (Direct computation of 50! and stripping zeros confirms the answer ends in 12.)
Final answer: 12

Final answer: 12

Write out 50! in full and delete all of its trailing zeros. The…

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