100!

Number Theory Level 3

Calculate the number of trailing zeroes in the following: (100!)(100!)(100!)(100!)(100!)...........................(100!) where there are 13!/30030 (100!)'s.

The answer is 4976640.

1 solution

Abyoso Hapsoro
Apr 8, 2015

First off, calculate $13! / 30030$ , you'll get 207360 Then we calculate the numbers of continuous 0's in 100!, $\left\lfloor \frac { 100 }{ 5 } \right\rfloor \quad +\quad \left\lfloor \frac { 100 }{ 25 } \right\rfloor \quad =\quad 20\quad +\quad 4\quad =\quad 24$ Then just multiply 207360 with 24, you get the answer 4976640

100!

The answer is 4976640.

1 solution

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