How many zeros in factorial 5000?

Answer 1

To determine the number of trailing zeros in (5000!), you can use the formula that counts the number of factors of 5 in the factorial. This is calculated as:

[ \left\lfloor \frac{5000}{5} \right\rfloor + \left\lfloor \frac{5000}{25} \right\rfloor + \left\lfloor \frac{5000}{125} \right\rfloor + \left\lfloor \frac{5000}{625} \right\rfloor ]

Calculating this gives:

[ 1000 + 200 + 40 + 8 = 1248 ]

Thus, (5000!) has 1248 trailing zeros.