# 最大公約数/因子（GCD）計算機

Enter numbers (comma-separated) or

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