ANOTHER RMO PROBLEM

Number Theory Level 2

Find the highest power of 3 which is contained in 500!

The answer is 247.

2 solutions

Anand Raj
Feb 25, 2014

$\left[ \frac { 500 }{ 3 } \right] +\left[ \frac { 166 }{ 3 } \right] +\left[ \frac { 55 }{ 3 } \right] +\left[ \frac { 18 }{ 3 } \right] +\left[ \frac { 6 }{ 3 } \right]$

= 166 + 55 + 18 + 6 + 2

= 247

can u please explain in more detail?

Dhruv G - 7 years, 3 months ago

You can search the net for Legendre's formula.

Satvik Golechha - 7 years, 3 months ago

Correct...... Actually I thought that the number was 50

Ritesh Mishra - 6 years, 11 months ago

Ajith Gade
Mar 23, 2014

(500/3 +500/(3.3) +500/(3.3.3) +500/(3.3.3.3) +500/(3.3.3.3.3) )

ANOTHER RMO PROBLEM

The answer is 247.

2 solutions

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