Plz tell me a proper logic for this question

#1

i am not able to think of a logic

#2

Hey @alter
Hint :

  • Make the number P using number N in form of an array.
  • Use PnC to find number of divisors of P .

Example :

  • Say N = 30
    2 3 5
    1 1 1
  • Now P = 1 * 2 * ....... * 30 = 810000
    You need to understand that divisors of N are combinations of 2, 3 & 5 .
    To make the array of P . You need to count the number of times 2, 3 & 5 will be picked in the divisors of N .
    As all the numbers are there only 1 time. there are 8 combinations of 2, 3 & 5 (000 001 010 011 100 101 110 111) where 0 means not picked and 1 means picked. We can see there are 8 divisors of 30 .
    Using this we can make the array for P .
    P = 810000
    2 3 5
    4 4 4
    Now finding the number of divisors of P is easy.
    000 001 002 003 004 010 011 012 013 014 ........... 442 443 444 these will be all the divisors of P where xyz means picking x of 2 , y of 3 and z of 5 .
    You can clearly see this is just a base 5 counting with 3 bits. so there will be 5^3 numbers b/w 000 .... 444 which is 125 .
    I hope this helps you.
#3

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