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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