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Calculatrice du plus grand commun diviseur/facteur (PGCD)

Trouver le plus grand commun diviseur pas à pas

La calculatrice déterminera le plus grand commun diviseur (PGCD) des nombres positifs donnés, avec les étapes détaillées, en utilisant soit la méthode de factorisation, soit la méthode de décomposition en facteurs premiers.

Enter numbers (comma-separated) or

Your input:

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

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

Note associée: Greatest Common Divisor (GCD)