Question

What is highest power of 8 contained in 80!?

Answer 1

I think nine is the highest power of 8 contained in 80!

Answer 2

The highest power of 8 contained in 80! is 32.

• If p is a prime number, then the highest power of p in a factorial x is given by:

$[\frac{x}{p} ]+[\frac{x}{p^{2} } ]+[\frac{x}{p^{3} } ]+....$

• 8 is expressed as $2^{3}$ in terms of a prime number
• Therefore, maximum power of $2^{3}$ in 80! according to the formula is 32.

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