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The least positive number such that the number of divisors of the number of divisors of the number of divisors of the number of divisors of the original number is \(3\).
 one year ago
 one year ago
The least positive number such that the number of divisors of the number of divisors of the number of divisors of the number of divisors of the original number is \(3\).
 one year ago
 one year ago

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ParthKohliBest ResponseYou've already chosen the best response.1
Now, I get \(72\) which is apparently wrong by doing repeated backwardworking. ``` 72 => 1,2,3,4,6,8,9,12,24,36,72   V 12 => 1,2,3,4,6,12   V 6 => 1,2,3,6   V 4 => 1,2,4   V 3 ```
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
So is there a number smaller than \(72\) which satisfies the conditions?
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
``` 60 = 2^2 * 3 * 5   V 12   V . . . ``` OMG, so 60 is the answer?!
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
I get how you did the last step by doing \(12 = 2 \cdot 2 \cdot 3\ \) :) I did the rest of the steps just like that!
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.1
60 is the least number with 12 divisors, I'll tell you how I remembered that. Gimme a min.
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
No, I know the divisor function. I was just doing least numbers throughout :)
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
For example, take \(2^2 3^1\). This number has \((2 + 1)(1 + 1) = 6\) divisors.
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
And to find the least number, you first prime factorize the number, then adjust the powers such that the least prime number gets the highest power and so on.
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
\[6 = 2\cdot 3 = 3\cdot 2 =6\cdot 1 =1 \cdot 6\]Now we can kinda see that it's evident how \(2^2 3^1\) is the least number. :)
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
I couldn't realize that we could take a product of three primes too :)
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
Do you know how divisor function works?
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.1
I had seen a very similar question on OS long time ago. That is how I could instantly say 60 ! :P Nevermind, I follow your reasoning very well. Kudos! B
 one year ago
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