Priemfactorisatie Rekenmachine

Wat is Priemfactorisatie Rekenmachine?

Formule

Hoe te berekenen

1. Enter any positive integer from 2 to 10,000,000.
2. The algorithm starts by dividing by 2, the smallest prime.
3. Each time the number divides evenly, the divisor is recorded as a factor.
4. When 2 no longer divides evenly, the algorithm tries 3, 5, 7, 11, ...
5. This continues until the remaining number equals 1 or is itself prime.
6. The factorization is written in exponential form: n = p₁^a₁ × p₂^a₂ × ...
7. Divisors are counted using the formula τ(n) = (a₁+1)(a₂+1)···(aₖ+1).

Voorbeeld

Sleutelbegrippen

Prime number

An integer > 1 with no factors other than 1 and itself

Composite number

An integer > 1 that is not prime

Fundamental Theorem of Arithmetic

Every integer > 1 has a unique prime factorization

Trial division

Factorization algorithm testing divisibility by successive primes

Exponent

In p^a, the exponent a counts how many times prime p appears

Divisor function τ(n)

Counts the total number of positive divisors of n

Veelvoorkomende toepassingen

• Particulieren die hun priemfactorisatie rekenmachine willen berekenen
• Professionals die snelle berekeningen nodig hebben
• Studenten die leren over priemfactorisatie rekenmachine
• Bedrijven die financiële analyses uitvoeren