Question

wt is the largest power of 3 in 150!

Answer 1

The largest power of 3 in 150 is 50.

Answer 2

Answer:

The largest power of 3 in 150! is 73.

Step-by-step explanation:

The highest power of 3 in (150)!

$\frac{150}{3} + \frac{150}{3^2} + \frac{150}{3^3} + \frac{150}{3^4}+----------$

Where [ ] is the greatest integer function.

$\frac{150}{3} + \frac{150}{3^2} + \frac{150}{3^3} + \frac{150}{3^4}+ \frac{150}{3^5}---------\\=\frac{150}{3} + \frac{150}{9} + \frac{150}{27} + \frac{150}{81}+ \frac{150}{81}+----------\\=50 + 16.66 + 5.55+ 2.22 + 0\\= 50 + 16 + 5 + 2\\= 73$

So, the largest power of 3 in 150! is 73.