There are 24 trailing zeros in 100 factorial.
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122 zeros.
To calculate the number of zeros in a factorial number, we need to determine the number of factors of 5 in the factorial. In this case, we are looking at 10 to the power of 10 factorial. The number of factors of 5 in 10! is 2 (from 5 and 10). Therefore, the number of zeros in 10 to the power of 10 factorial would be 2.
To determine the number of trailing zeros in 85 factorial (85!), you count how many times 5 is a factor in the numbers from 1 to 85, as there are always more factors of 2 than 5. This is calculated using the formula: [ \text{Number of trailing zeros} = \left\lfloor \frac{85}{5} \right\rfloor + \left\lfloor \frac{85}{25} \right\rfloor = 17 + 3 = 20. ] Thus, 85! has 20 trailing zeros.
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.
Exactly as in the question. There is no need for a decimal point and trailing zeros.Exactly as in the question. There is no need for a decimal point and trailing zeros.Exactly as in the question. There is no need for a decimal point and trailing zeros.Exactly as in the question. There is no need for a decimal point and trailing zeros.