The number of odd divisors of $2^{200}$ is 

If any number is in the form of $2^k\left(k\in N\right)$ , then number of odd divisors is$1$

For ex: Number of odd divisors of $16$

$16=2^4$  divisors of 16 are $\text{1},\text{2},\text{4},\text{8},\text{16}$

$‘\text{1}’$ is only the odd divisor

$\therefore$  The Number of odd divisors of $\text{16}$  is $1$