Prime Factorization
Decompose any positive integer into its prime factors. View the result as a product, step-by-step division, factor tree, and total number of divisors.
How to Find Prime Factorization
- Enter any positive integer in the input field.
- Click Factorize — the calculator divides by primes starting from 2.
- View the result as a compact product (e.g., 2² × 3 × 5) and the step-by-step division.
- Check the factor tree and total divisor count for additional insight.
快速参考
| 从 | 到 |
|---|---|
| 12 | 2² × 3 |
| 30 | 2 × 3 × 5 |
| 100 | 2² × 5² |
| 56 | 2³ × 7 |
| 84 | 2² × 3 × 7 |
| 360 | 2³ × 3² × 5 |
使用场景
- •Simplifying fractions — factorize numerator and denominator to find and cancel common factors.
- •Cryptography — understand the difficulty of factoring large numbers that underlies RSA encryption.
- •Number theory — verify whether two numbers are coprime by checking if their GCD equals 1.
公式
Every integer greater than 1 can be uniquely represented as a product of prime numbers (Fundamental Theorem of Arithmetic). The total number of divisors equals the product of (exponent + 1) for each prime factor.
常见问题
What is a prime number?
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The first few primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
How do you find the prime factorization of a number?
Divide the number by the smallest prime (2), repeating while it divides evenly. Then try 3, then 5, and so on. Continue until the quotient is 1. For example, 60 = 2² × 3 × 5.
How do you calculate the total number of divisors?
If n = p₁^a₁ × p₂^a₂ × ... then the number of divisors is (a₁+1)(a₂+1).... For example, 60 = 2² × 3¹ × 5¹ has (2+1)(1+1)(1+1) = 12 divisors.