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 2 years 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 \(3\).
 2 years 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 \(3\).

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ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1Now, 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 ```

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1So is there a number smaller than \(72\) which satisfies the conditions?

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

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1I 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!

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.160 is the least number with 12 divisors, I'll tell you how I remembered that. Gimme a min.

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1No, I know the divisor function. I was just doing least numbers throughout :)

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

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1And 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.

ParthKohli
 2 years ago
Best 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. :)

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1I couldn't realize that we could take a product of three primes too :)

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1Do you know how divisor function works?

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.1I 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
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