 # Python Program to Compute Prime Factors of an Integer

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In this post, we’ll look at a Python program that prints out all the prime factors of a given number. A number is considered to be a prime factor of another number if it is a prime number and perfectly divides the given number. In this section, we will look at what a prime factor is, how to discover a prime factor, and the python program.

A number’s prime factors are the prime numbers that, when multiplied together, give the number. Two conditions can be used to determine a number’s prime factor:

The digit should be a prime number.

The number should perfectly divide the number.

Examples:

Example1:

Input:

given number =240

Output:

The prime factors of the given number are :
2
3
5

Example2:

Input:

given number =33

Output:

Enter some random number = 33
The prime factors of the given number are :
3
11

## Program to Compute Prime Factors of an Integer in Python

There are several ways to compute prime factors of an integer in python some of them are:

### Method #1: Using while loop (Static Input)

Approach:

• Give the integer value as static input.
• Using a while loop, first determine the number’s components.
• Calculate whether the factors are prime or not using another while loop within the previous one.
• Exit of program.

Below is the implementation:

# given number
numb = 240
# Printing the prime factors
print("The prime factors of the given number are : ")
value = 1
while(value <= numb):
k = 0
if(numb % value == 0):
j = 1
while(j <= value):
if(value % j == 0):
k = k+1
j = j+1
if(k == 2):
# printing the prime factor
print(value)
# incremeent the value by 1
value = value+1


Output:

The prime factors of the given number are :
2
3
5

Explanation:

• Given the number as static input.
• The while loop is utilized, and the integer factors are obtained by using the modulus operator and determining whether the remainder of the number divided by value is zero.
• The integer’s factors are then checked again to see if they are prime.
• The factor of an integer is prime if it has two factors.
• The integer’s prime factor is printed.

### Method #2: Using while loop (User Input)

Approach:

• Scan the number using int(input()) function.
• Using a while loop, first determine the number’s components.
• Calculate whether the factors are prime or not using another while loop within the previous one.
• Exit of program.

Below is the implementation:

# Scan the number using int(input()) function.
numb = int(input("Enter some random number = "))
# Printing the prime factors
print("The prime factors of the given number are : ")
value = 1
while(value <= numb):
k = 0
if(numb % value == 0):
j = 1
while(j <= value):
if(value % j == 0):
k = k+1
j = j+1
if(k == 2):
# printing the prime factor
print(value)
# incremeent the value by 1
value = value+1


Output:

Enter some random number = 220
The prime factors of the given number are :
2
5
11

### Method #3:Efficient Method (User input)

Approach:

• Scan the given number using int(input()) function.
• We will print 2 and divide numb by 2 while it is divisible by 2.
• Following step 2, numb must always be odd.
• Begin a loop with I = 3 and work your way up to the square root of n. If I divide numb by I print I and divide numb by i. If we  unable to divide numb , increase the I value by 2 and proceed.
• If numb is a prime number and higher than 2, it cannot be reduced to 1.
• So, if numb is larger than 2, print it.

Below is the implementation:

import math
# Scan the number using int(input()) function.
numb = int(input("Enter some random number = "))
# Printing the prime factors
print("The prime factors of the given number are : ")
while numb % 2 == 0:
print(2),
numb = numb / 2

# n became odd
for i in range(3,int(math.sqrt(numb))+1,2):
while (numb % i == 0):
print (int(i))
numb = numb / i

if numb > 2:
print (int(numb))


Output:

Enter some random number = 33
The prime factors of the given number are :
3
11

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