Numbers by Prabhav (Part:2)

Number Theory Level 3

Find the highest power of 3 contained in 1000!


The answer is 498.

Prabhav Bansal by Prabhav Bansal , 28, India

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1 solution

Department 8
Sep 5, 2015

The highest power of a a contained in n ! n! is given by

p ( a ) = ∑ k = 1 ∞ ⌊ n a k ⌋ p(a) = \sum _{ k=1 }^{ \infty }{ \left\lfloor \frac { n }{ { a }^{ k } } \right\rfloor }

At last you will get your answer as 498.

4 Helpful 0 Interesting 0 Brilliant 0 Confused

Why is it a level 4 problem ? It should be level 1.

Swapnil Das - 5 years, 9 months ago

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