免费质因数分解计算器
将任意正整数分解为质因数之积。
Sqrt N
9.1652
公式
Prime Factorization
What Is It?
Every integer greater than 1 can be written as a product of prime numbers in exactly one way (Fundamental Theorem of Arithmetic).
Method: Trial Division
1. Start with the smallest prime (2) 2. If it divides the number, it is a factor; divide and repeat 3. If not, try the next prime (3, 5, 7, 11, ...) 4. Stop when you reach sqrt(n)
Divisibility Quick Checks
This calculator shows divisibility checks. For full factorization of large numbers, a step-by-step approach is needed.
计算示例
Check divisibility of 84.
- 0184 / 2 = 42 (divisible by 2)
- 0284 / 3 = 28 (divisible by 3)
- 0384 / 5 = 16.8 (not divisible by 5)
- 0484 / 7 = 12 (divisible by 7)
- 0584 = 2² × 3 × 7
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. Examples: 2, 3, 5, 7, 11, 13...
What is the fundamental theorem of arithmetic?
Every integer greater than 1 is either prime or can be written as a unique product of prime numbers (up to ordering).
Why do we only check up to sqrt(n)?
If n has a factor larger than sqrt(n), it must also have a corresponding factor smaller than sqrt(n). So checking up to sqrt(n) is sufficient.
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