Radeen10-_

Prime in Numbers with Wheel Factorization

Sep 14th, 2021
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  1.  
  2. Given a positive number n > 1 find the prime factor decomposition of n. The result will be a string with the following form :
  3.  
  4. "(p1**n1)(p2**n2)...(pk**nk)"
  5. with the p(i) in increasing order and n(i) empty if n(i) is 1.
  6. @EXAMPLE:
  7. n = 86240 should return "(2**5)(5)(7**2)(11)"
  8. n= 782611830 should return "(2)(3**2)(5)(7**2)(11)(13)(17)(73)"
  9.  
  10.  
  11. -------------------------------------------------------------------------------------------------------------------------------------
  12.  
  13.  
  14.  
  15. import math
  16.  
  17. def prime_factors(n):
  18.     result=''
  19.     count = 0
  20.     while n%2==0:
  21.         n/=2
  22.         count+=1
  23.     if count==1:
  24.         x2=("("+"2"+")")
  25.         for cnt01 in x2:
  26.             result+=cnt01
  27.     elif count:
  28.         x= ("(" + "2**" + str(count) + ")" )
  29.         for cnt02 in x:
  30.             result+=cnt02
  31.  
  32.  
  33.     for k in range(3,int(math.sqrt(n)+1),2):
  34.         count=0
  35.         while n%k==0 and n!=1:
  36.             n/=k
  37.             count+=1
  38.         if count==1:
  39.             z=("("+str(k)+")")
  40.             for cnt in z:
  41.                 result+=cnt
  42.  
  43.         elif count:
  44.             y= ("("+str(k) + "**" + str(count)+")")
  45.             for cnt1 in y:
  46.                 result+=cnt1
  47.     if n > 2:
  48.         x1=("("+str(int(n))+")")
  49.         for cnt2 in x1:
  50.             result+=cnt2
  51.            
  52.     return result
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