Prime Factorization API: Calculate Prime Factors

Need to decompose numbers into their prime factors? The Prime Factorization API breaks down any integer into its prime constituents, returning the complete factorization with exponents and formatted representations.

What is Prime Factorization?

Prime factorization is the process of finding which prime numbers multiply together to make a given number. Every integer greater than 1 has a unique prime factorization (this is the Fundamental Theorem of Arithmetic).

Examples:

• 12 = 2 x 2 x 3 = 2^2 x 3
• 100 = 2 x 2 x 5 x 5 = 2^2 x 5^2
• 17 = 17 (prime, only factor is itself)

How Prime Factorization Works

The API uses efficient factorization algorithms:

Trial Division

For smaller numbers, systematically testing potential prime factors starting from 2.

Pollard's Rho Algorithm

For larger numbers, using probabilistic methods for faster factorization.

Miller-Rabin Primality Test

Quickly determining if remaining factors are prime.

Using the Prime Factorization API

TinyFn provides a simple endpoint for prime factorization:

GET https://api.tinyfn.io/v1/math/prime-factors?number=360
Headers: X-API-Key: your-api-key

{
  "number": 360,
  "factors": [2, 2, 2, 3, 3, 5],
  "unique_factors": [2, 3, 5],
  "factorization": {
    "2": 3,
    "3": 2,
    "5": 1
  },
  "formatted": "2^3 x 3^2 x 5",
  "is_prime": false,
  "factor_count": 6
}

Parameters

Code Examples

JavaScript / Node.js

const response = await fetch(
  'https://api.tinyfn.io/v1/math/prime-factors?number=84',
  { headers: { 'X-API-Key': 'your-api-key' } }
);
const data = await response.json();
console.log(`Factors: ${data.factors.join(' x ')}`); // 2 x 2 x 3 x 7
console.log(`Formatted: ${data.formatted}`); // 2^2 x 3 x 7

Python

import requests

response = requests.get(
    'https://api.tinyfn.io/v1/math/prime-factors',
    headers={'X-API-Key': 'your-api-key'},
    params={'number': 1000}
)
data = response.json()
print(f"1000 = {data['formatted']}")  # 2^3 x 5^3
print(f"Unique primes: {data['unique_factors']}")  # [2, 5]

cURL

curl "https://api.tinyfn.io/v1/math/prime-factors?number=360" \
  -H "X-API-Key: your-api-key"

Common Use Cases

• Educational Apps: Teach prime factorization concepts
• Math Homework Helpers: Verify student answers
• Cryptography: Understand number structure for encryption
• GCD/LCM Calculators: Prime factors enable efficient GCD/LCM computation
• Number Theory Research: Analyze properties of integers

Best Practices

1. Validate input: Ensure numbers are positive integers greater than 1
2. Handle primes: Prime numbers return themselves as the only factor
3. Consider size limits: Very large numbers may timeout
4. Use appropriate format: Exponential form for display, array for computation
5. Cache common factorizations: Small numbers are frequently requested