I assume factors means divisors, since prime is not mentioned.

87,178,291,200 = 2^11 * 3^5 * 5^2 * 7^2 * 11 * 13

 

therefore  87,178,291,200 has 12*6*3*3*2*2 = 2592 factors (divisors).

For a number to have exactly 3 divisors it must be the square of a prime. The square root of 10^11 is  316227.766016838 so we need to square a prime that is less than or equal to  316227. The answer is  316223^2 =  99996985729.