Greatest Common Divisor/Factor (GCD) Calculator

The calculator will find the greatest common factor/divisor (GCF) of the given positive numbers, with steps shown, using either the factoring method or the prime factorization method.

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 write it in the comments below.

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