Discussion

Explanation:

288 = 2⁵ × 3²

The highest power of 3 in 35! is $R\left[\frac{35}{3}\right]$ + $R\left[\frac{35}{3^2}\right]$ + $R\left[\frac{35}{3^3}\right]$ = 11 + 3 + 1 = 15.

∴ The highest power of 3² will be $\frac{15}{2}$ = 7.

The highest power of 2 in 35! is $R\left[\frac{35}{2}\right]$ + $R\left[\frac{35}{2^2}\right]$ + $R\left[\frac{35}{2^3}\right]$ + $R\left[\frac{35}{2^4}\right]$ = 17 + 8 + 4 + 2 + 1 = 32.

∴ The highest power of 2⁵ will be $\frac{32}{5}$ = 6.

⇒ The highest power of 288 will be lower of 7 and 6 i.e., 6.

Hence, option (b).

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