Correct Answer - Option 2 : 87
Given:
n lies between 355 and 360
Concept Used:
n! = n(n – 1)(n – 2)…1
Number of zeros = Power of 5
In the case of factorial, the power of 5 is the limiting factor because 5 is less likely to occur than 2.
Maximum power of 5 in n! = n/5 + n/52 + n/53 +... (Consider integer values only)
Calculation:
We can pick any value from 356, 357, 358, and 359. The number of zeros will be the same for any value because 5 does not occur from 356 to 359.
Let n = 359
359! = 359 × 358 × … × 1
Maximum power of 5 in 359! = 359/5 + 359/52 + 359/53 = 71 + 14 + 2 = 87
Here we consider integer values only and ignore the remainder.
∴ The number of zeros is 87.