Playing With Divisors Is Fun

#1

please i cannot able to solve it
any help would be appreciated.

#2

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

how to find x,y,zā€¦ please explain. I mean the powers of prime numbers in P.

#4

using combinations of current divisors. See in these 8 combinations the is ā€˜1ā€™ at each possition 4 times.

#5

Thanx , Rated you 5 star.

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