Question

Find the highest power of 3 contained in 50! ?
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Answer 1

Answer:

Three is the highest power of 3 which gives 27 contained in 50..

Step-by-step explanation:

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Answer 2

The highest power of 3 contained in 50! is 22.

Given:

Factorial of 50

To find:

The highest power of 3 in 50 factorial

Solution:

The detailed mathematical explanation along with the steps is given below:

For finding the highest power of a prime number in a factorial, remember:

Greatest integer less than or equal to x ---> [x]

For example, greatest integer less than or equal to 5.3 ---> 5

So similarly calculating the factorial of 50 with 3, we get:

= $[\frac{50}{3}]+[\frac{50}{3^{2} }]+[\frac{50}{3^{3} }]+[\frac{50}{3^{4} }]+....$

=    $[\frac{50}{3}]+[\frac{50}{9}]+[\frac{50}{27}]+[\frac{50}{81}]+....$

= 16 + 5 + 1 + 0

= 22

Therefore, the highest power of 3 contained in 50 is 22.