Calculadora de Fatores Online Grátis
All factors and prime factorization of any integer with visual breakdown
The Factor Calculator finds all positive divisors of any integer and presents its complete prime factorization in exponential notation. It shows a factor tree breakdown that makes the factorization process visually clear. Number theory students, teachers explaining divisibility, and anyone working with fractions or GCF/LCM problems will find this tool directly useful.
Frequently Asked Questions
Sobre Esta Calculadora
Every positive integer greater than 1 can be uniquely expressed as a product of prime numbers — this is the Fundamental Theorem of Arithmetic. Finding a number's prime factorization reveals its full divisibility structure: the total number of factors can be computed directly from the exponents in the prime factorization.
This calculator finds all factors by trial division up to √n, then lists them in pairs. Simultaneously it builds the prime factorization by extracting the smallest prime factor repeatedly until the quotient is 1. The result shows both the complete factor list and the compact exponential form (e.g., 360 = 2³ × 3² × 5).
Factor analysis is used in simplifying fractions, computing GCF and LCM, solving modular arithmetic problems, and understanding number patterns. In cryptography, the difficulty of factoring large numbers is the foundation of RSA security. For students, it's one of the core number theory skills tested in standardized exams.
Resolva os divisores das suas matrizes fatoradas sem percalços no cálculo absoluto.
Exemplo Resolvido
Finding all factors and prime factorization of 360
Entradas:
- Number: 360
Passo a Passo:
- Divide by smallest prime (2): 360 ÷ 2 = 180
- 180 ÷ 2 = 90
- 90 ÷ 2 = 45
- 45 ÷ 3 = 15
- 15 ÷ 3 = 5
- 5 is prime → stop
- Prime factorization: 2³ × 3² × 5
- Total factors: (3+1)×(2+1)×(1+1) = 4×3×2 = 24 factors
- All factors: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360