# 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.

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