Kalkulator rozkładu na czynniki pierwsze
Wprowadź liczbę naturalną w pole aby poznać jej czynniki pierwsze.
Czynniki pierwsze to: 2, 5
Czynnik pierwszy to dowolna liczba pierwsza, która dzieli bez reszty daną liczbę naturalną złożoną.
Przedstawienie danej liczby złożonej w postaci iloczynu czynników pierwszych nazywamy rozkładem liczby na czynniki pierwsze. Rozkład ten jest jednoznaczny w tym sensie, że każde inne rozkłady danej liczby na czynniki pierwsze różnią się tylko kolejnością czynników. Na przykład dla liczby 20: $20=2⋅2⋅5=5⋅2⋅2=2⋅5⋅2=2^2⋅5$.
Zgodnie z "podstawowym twierdzeniem arytmetyki" każda liczba naturalna większa od 1 jest albo pierwsza, albo ma przynajmniej jeden czynnik pierwszy. Wynika stąd dalej, że każda liczba naturalna większa od 1 jest pierwsza lub daje się zapisać w postaci iloczynu liczb pierwszych.
Przedstawienie danej liczby złożonej w postaci iloczynu czynników pierwszych nazywamy rozkładem liczby na czynniki pierwsze. Rozkład ten jest jednoznaczny w tym sensie, że każde inne rozkłady danej liczby na czynniki pierwsze różnią się tylko kolejnością czynników. Na przykład dla liczby 20: $20=2⋅2⋅5=5⋅2⋅2=2⋅5⋅2=2^2⋅5$.
Zgodnie z "podstawowym twierdzeniem arytmetyki" każda liczba naturalna większa od 1 jest albo pierwsza, albo ma przynajmniej jeden czynnik pierwszy. Wynika stąd dalej, że każda liczba naturalna większa od 1 jest pierwsza lub daje się zapisać w postaci iloczynu liczb pierwszych.
Zobacz również
Polecany kalkulator rozkładu na czynniki pierwsze (22)
to działa xD
15
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