How to Find prime factor of a number

Find Prime factor of a number is one of most common question  encounter in basic mathematics . But it has very high uses not only in mathematics problems but also in high level algorithmic programming problems. Mostly problems that uses properties of numbers .
If you wan't to become a programmer ,you will face many problems that uses properties of numbers , and we know a good programmer always try to find best way to solve problem otherwise there is always a straight way (Brute force way ) to solve almost any problem .
But we know it will ruin speed of  programming  result  that's why we always try to find fastest and effective way to solve problems .

Algorithm to Find prime factor of a number :

It uses very basic concept of division

1. Let number is n
2. Set encounter to 2 (i.e i=2)
3. Now divide n by i

       If  n is divisible by i  :- put it in list or array let say it pf 

        then update value of n by n/i (n = n/i)

         then go to step 3 again 

      Else :- continue

4. Now check if  i > squire root of n :-then stop iterating and exit
5. Else : increment counter by 1 ( i = i+1) and goto step 3

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Python Program to Find prime factor of a number :

1. # Find prime factor of a number
2. # http://beginer2cs.blogspot.com
3. # Python 2.7
5. import math
7. def prime_fact(n):
8.     '''
9.        return a list ,contain prime factor of n
10.    '''
11.     flag=True # we Use this to continue or come out from while loop
12.     pf=[]
13.     i=2 # we start iteration from 2 (just as an counter)
14.     sq = math.sqrt(n) # this is end point of iteration ( Think why ??)
15.    
16.     while(flag): #start iteration
17.         if n%i == 0: #if i is  factor of n
18.             pf.append(i) #then append it in list
19.             n=n/i  #and update value of n by n/i
20.            
21.         elif i>sq : #test for end of iteration
22.             flag =False
23.            
24.         else:
25.             i = i+1 # increment counter by 1
27.     return pf
29. if __name__=='__main__':
30.     n=int(raw_input('Enter ur number : '))
31.     print prime_fact(n)

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Output :