Question

The probability that a randomly selected three-digit number has exactly three factors will be ............

• A. $\frac{7}{900}$
• B. $\frac{5}{900}$
• C. $\frac{11}{900}$
• D. $\frac{16}{900}$

Answer 1

The correct option is A $\frac{7}{900}$

We need a number having only $3$ factors.
For any general composite number, we have even number of factors since two numbers need to be multiplied to get the answer.
However, for square numbers, we get odd number of factors.
Also since we are in need of numbers having only $3$ factors, the numbers will have to be squares of prime numbers.
The square of $10$ is $100$, the smallest 3 digit number whereas the square of $31$ is $961$, the largest square number.
Now from $10$ to $31$, there are $11,13,17,19,23,29,31$ i.e. $7$ prime numbers.
Hence, the probability comes out to be $\frac{7}{900}$