Python Program for Find largest prime factor of a number

Last Updated : 14 Mar, 2023

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: $\text{O}(\sqrt{n})$
Auxiliary space: $\text{O}(1)$
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)) 