$32 \cdot 21$ Among the positive integers less than 50, the number of integers that have an odd number of positive integer factors is
(A) 3 .
(B) 5 .
(C) 7 .
(D) 9 .
(E) 11 .
(41st American High School Mathematics Examination, 1990)
[Solution 1] By the Sieve of Eratosthenes, the prime factors of positive integers less than 50 do not exceed $\sqrt{50}$.
Thus, these factors are $1,2,3,5,7$.
A number with an odd number of positive integer factors should, apart from the factor 1, also have an even number of factors. Therefore, such integers should be even powers of the aforementioned primes, i.e.,
$$
2^{2}, 3^{2}, 5^{2}, 7^{2}, 2^{2} \cdot 3^{2}, 2^{4} ;
$$

In addition, there is 1, making a total of 7.
Therefore, the answer is $(C)$.
[Solution 2] A natural number with an odd number of positive integer factors must be a perfect square. Among the positive integers less than 50, there are 7 perfect squares $(\sqrt{50} \approx 7)$.
Therefore, the answer is $(C)$.