# Python Program for Find largest prime factor of a number

Given a positive integer \’n\'( 1 <= n <= 1015). Find the largest prime factor of a number.

Input: 6
Output: 3
Explanation
Prime factor of 6 are- 2, 3
Largest of them is 3

Input: 15
Output: 5

## Python3

 # Python3 code to find largest prime  # factor of number  import math     # A function to find largest prime factor  def maxPrimeFactors (n):             # Initialize the maximum prime factor      # variable with the lowest one      maxPrime = -1            # Print the number of 2s that divide n      while n % 2 == 0:          maxPrime = 2         n >>= 1     # equivalent to n /= 2                 # n must be odd at this point,       # thus skip the even numbers and       # iterate only for odd integers      for i in range(3, int(math.sqrt(n)) + 1, 2):          while n % i == 0:              maxPrime = i              n = n / i             # This condition is to handle the       # case when n is a prime number       # greater than 2      if n > 2:          maxPrime = n             return int(maxPrime)     # Driver code to test above function  n = 15 print(maxPrimeFactors(n))     n = 25698751364526 print(maxPrimeFactors(n))     # This code is contributed by "Sharad_Bhardwaj".

Output

5
328513


Time complexity:
Auxiliary space:
Please refer complete article on Find largest prime factor of a number for more details!

Method 2:

Follow the steps below for the implementation:

• Initialize variables largest_prime to -1, i to 2, and n to the input integer.
• Start a while loop that continues as long as i * i <= n. This loop will iterate through all possible factors of n.
• In the while loop, start another while loop that continues as long as n % i == 0. This inner loop will divide n by i until n is no longer divisible by i.
• In the inner loop, set largest_prime to i, and update n by dividing it by i.
• At the end of the inner loop, increment i by 1.
• After the outer loop, if n > 1, set largest_prime to n. This is because n could be a prime number larger than any of its factors.
• Return largest_prime.

## Python3

 def largest_prime_factor(n):      """      Find the largest prime factor of a positive integer 'n'      :param n: positive integer ( 1 <= n <= 10^15)      :return: largest prime factor of n      """     largest_prime = -1     i = 2     while i * i <= n:          while n % i == 0:              largest_prime = i              n = n // i          i = i + 1     if n > 1:          largest_prime = n      return largest_prime     n = 15 print(largest_prime_factor(n))     n = 25698751364526 print(largest_prime_factor(n))

Output

5
328513


Time complexity:  O(sqrt(n)).
Auxiliary space: O(1),

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