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Rechner für den größten gemeinsamen Teiler (ggT)

Finde den größten gemeinsamen Teiler Schritt für Schritt

Der Rechner ermittelt den größten gemeinsamen Teiler (ggT) der gegebenen positiven Zahlen und zeigt dabei die Lösungsschritte, entweder durch Auflisten der Teiler oder mittels Primfaktorzerlegung.

Enter numbers (comma-separated) or

Your input:

Positive numbers separated by commas, for example, `12,24,32,40,28`.

Choose a method:

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please contact us.

Solution

Your input: find the GCD of $$$30, 60, 45, 105, 25$$$ using factoring.

The GCD of numbers is the largest number that divides all given numbers.

Find the factors/divisors of each number.

  • The factors of $$$\color{Green}{30}$$$: $$$1, 2, 3, \color{Red}{5}, 6, 10, 15, 30$$$
  • The factors of $$$\color{Green}{60}$$$: $$$1, 2, 3, 4, \color{Red}{5}, 6, 10, 12, 15, 20, 30, 60$$$
  • The factors of $$$\color{Green}{45}$$$: $$$1, 3, \color{Red}{5}, 9, 15, 45$$$
  • The factors of $$$\color{Green}{105}$$$: $$$1, 3, \color{Red}{5}, 7, 15, 21, 35, 105$$$
  • The factors of $$$\color{Green}{25}$$$: $$$1, \color{Red}{5}, 25$$$

The greatest common (all numbers share it) factor/divisor is highlighted.

Thus, $$$GCD\left(30, 60, 45, 105, 25\right)=5$$$.

Answer: $$$GCD\left(30, 60, 45, 105, 25\right)=5$$$.

Verwandter Hinweis: Greatest Common Divisor (GCD)