1. How many factors has 87,178,291,200 ?
2. What is the biggest number below 10^11 with only 3 factors>?
3. How are the above questions related?
4. ...and the title?
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.

Posted by Charlie
on 20190522 12:29:57 