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Soft car for cats (Posted on 2019-05-22) Difficulty: 3 of 5
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?

No Solution Yet Submitted by Ady TZIDON    
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Some Thoughts partway, I think | Comment 1 of 2
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 2019-05-22 12:29:57
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