Question

Find the highest power of 2 contained in 150!

• A. 148
• B. 146
• C. 147
• D. 145

Answer 1

The correct option is B 146

Highest power of 2 in $\left(150\right)!$

$\left[\frac{150}{2}\right]+\left[\frac{150}{2^2}\right]+\left[\frac{150}{2^3}\right]+\left[\frac{150}{2^4}\right]+\left[\frac{150}{2^5}\right]+\left[\frac{150}{2^6}\right]+\left[\frac{150}{2^7}\right]+...$ , where $\left[\right]$ is greatest integer function.

$=\left[75\right]+\left[37.5\right]+\left[18.75\right]+\left[9.375\right]+\left[4.688\right]+\left[2.344\right]+\left[1.172\right]+\left[0.58\right]+...=75+37+18+9+4+2+1+0=146$