Prime Factors of a Number in C, C++, Java & Python – Code with Explanation & Examples in Short and Simple

   

C Program

void primeFactors(int n) {
    for (int i = 2; i <= n; i++)
        while (n % i == 0) {
            printf("%d ", i);
            n /= i;
        }
}

C Output

Input:  
60 

Output:  
2 2 3 5

C++ Program

void primeFactors(int n) {
    for (int i = 2; i <= n; i++)
        while (n % i == 0) {
            cout << i << " ";
            n /= i;
        }
}

C++ Output

Input:  
84  

Output:  
2 2 3 7

JAVA Program

void primeFactors(int n) {
    for (int i = 2; i <= n; i++)
        while (n % i == 0) {
            System.out.print(i + " ");
            n /= i;
        }
}

JAVA Output

Input:  
100  

Output:  
2 2 5 5

Python Program

def prime_factors(n):
    i = 2
    while i <= n:
        if n % i == 0:
            print(i, end=' ')
            n //= i
        else:
            i += 1

Python Output

Input:  
90  

Output:  
2 3 3 5

In-Depth Explanation

Example

Let's take n = 60.

The prime factors are:

60 ÷ 2 = 30

30 ÷ 2 = 15

15 ÷ 3 = 5

5 ÷ 5 = 1

So the result is: 2 2 3 5

Each of these is a prime number, and their product is 60.

Real-Life Analogy

Imagine a number as a huge "bundle" of tiny boxes stacked on top of each other. Prime factors are the bricks or atoms which cannot be divided further and multiply back to form the initial number. It is similar to dissociating a compound into its simplest chemical constituents.

For instance, in baking, if you produce 60 cookies by repeating lots, the smallest repeatable pack (prime factor) informs you about the recipe structure — the basic units that multiply to the total.

Why It Matters

Prime factorization is applied in:

Cryptography (RSA Encryption)

Number theory problems

Finding GCD, LCM

Reducing fractions to lowest terms

It is crucial in mathematics, logic design, and data encryption systems to know how a number is composed of prime parts.

What You'll Learn from This

You know:

Looping with conditionals (while)

Division and modulo operations

Efficient number deconstruction

Properties of primes

It also shows you how to handle factorization, something applied in several programming situations such as matrix operations, polynomial reductions, and algorithm optimizations.

Interview Relevance and Actual Projects

Interviewers apply this to probe:

Your knowledge of loops

Mathematical problem-solving reasoning

Optimization ability of factor checks

In actual application:

Banking applications can employ cryptographic mathematics beginning with factoring

Game scoring mechanisms or resource dividers require even divisibility rules

Learning resources apply this to instruct students in basic arithmetic concepts

SEO-Optimized Explanation

Prime factorization in C, C++, Java, and Python is a basic programming exercise applied to divide a number into its prime factors. It aids in the learning of number decomposition, loops, and modulus-based programming concepts. It's critical in competitive programming, cryptographic use, GCD/LCM computation, and elementary number theory questions. By decomposing a number through repeated division, you find its underlying prime factors, which is an incredibly strong idea in both math and computer science. Having a strong grasp of this problem solidifies the building of logic and readies you for actual challenges with encryption, system tuning, and computer algorithms.