Prime Factorization Calculator
Analyze a number for prime properties. Shows the smallest prime factor, number of factors, and divisibility checks.
Sqrt N
9.1652
Formula
## 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 - **By 2**: last digit is even - **By 3**: digit sum is divisible by 3 - **By 5**: last digit is 0 or 5 This calculator shows divisibility checks. For full factorization of large numbers, a step-by-step approach is needed.
Exemplo Resolvido
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
Perguntas Frequentes
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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