Question

How many numbers less than $2^{24}$ are co prime to it?

• A. $2^{12}$
• B. $2^{23}$
• C. $2^{22}$
• D. None of these

Answer 1

Answer: (B)

$2^{23}$

Using Euler's Formula,
Number of co-primes less than $2^{24}=n[1-\frac{1}{p}]$
$=2^{24}[1-\frac{1}{2}]=\frac{2^{24}}{2}$
$=2^{23}$