Find Prime Factors Of A Number in Python

You might have heard about factors of a number. Factors of any given number are those numbers that divide the given number completely leaving no remainder. In this article, we will discuss an algorithm to find prime factors of a number in python.

What Are Prime Factors Of A Number?

Prime numbers are those numbers that have only two factors, 1 and the number itself. Also, we can represent any given number as a product of prime numbers. Here, all those prime numbers that we can use to represent any given number are called the prime factors of the given number.

For instance, we can represent 20 as the product of prime number 2 and 5 as 2x2x5. Hence, 2 and 5 are prime factors of 20. Similarly, we can represent any number using a combination of prime numbers.

Algorithm To Find Prime Factors Of A Number

To find the prime factors of a number, we just have to divide the given number using prime numbers. But, how do we know if a factor of the given number is prime or not? To eliminate this problem, we will use repetitive division. Let us take the number 1260 as our running example so that we can find its prime factors.

First, we will divide the given number repetitively by 2 and store the resultant number until the remainder becomes 1. By this, we will make sure that any even number will not divide the resultant. Now, we can skip all the even numbers while finding the factors of the given number. For instance, we will divide 1260 by 2, two times, giving 315 as resultant. Here, you can see that the resultant 315 is an odd number. Hence no even number can be its factor. 

After division by 2, we will repetitively divide the resultant by 3 and store the result until the number becomes indivisible by 3.  By this, we will make sure that any multiple of 3 will not divide the resultant. Here, we will divide 315 by 3, two times, giving 35 as resultant. You can see that no multiple of 3 can divide 35. 

Similarly, we will perform repetitive division using 5,7,9, 11, and other odd numbers until the resultant becomes 1. In this way, we can find the prime factors of any given number. Here, 1260 has 2, 3, 5, and 7 as its prime factors.

Python Program To Find Prime Factors Of A Number

Now, we will implement the algorithm discussed above to find the prime factors of any given number. Here, we will create a set to store the prime factors and implement the above algorithm as follows.

def calculate_prime_factors(N):
    prime_factors = set()
    if N % 2 == 0:
        prime_factors.add(2)
    while N % 2 == 0:
        N = N // 2
        if N == 1:
            return prime_factors
    for factor in range(3, N + 1, 2):
        if N % factor == 0:
            prime_factors.add(factor)
            while N % factor == 0:
                N = N // factor
                if N == 1:
                    return prime_factors


input_number = 20
output = calculate_prime_factors(input_number)
print("Prime factors of {} are {}".format(input_number, output))
input_number = 1260
output = calculate_prime_factors(input_number)
print("Prime factors of {} are {}".format(input_number, output))

Output:

Prime factors of 20 are {2, 5}
Prime factors of 1260 are {2, 3, 5, 7}

Conclusion

In this article, we have discussed and implemented an algorithm to find the prime factors of a given number in python. To learn more about numbers in python, you can read this article on decimal numbers in python. You might also like this article on complex numbers in python.