# GCD / polynomial GCD online calculator: Calculate the greatest common divisor of integers and polynomials

The `gcd`

command produces the GCD of integers and polynomials. If you write `gcd 12 16`

in the form above, the calculator will output 2 as follows.

GCD is the greatest common divisor and the GCD of 12 and 16 is 4. 1, 2, 4 are the divisors of them and 4 is the greatest one. The calculator can't take decimals such as 3.9 because it's not an integer. You can find the GCD of three or more integers in this online calculator.

```
gcd 12 16 24
```

The calculator shows 4. All numbers need separated by comma or space. So both `gcd 12, 16`

and `gcd 12 16`

are valid.

## Polynomial GCD

We can find the GCD polynomials of two or more polynomials whose coefficients are all integers. X, Y are polynomials and can be factored like this.

X = ABC, Y=ABD

A, B, C, D are polynomials that can't be factored. Then A and B are the common polynomial divisors so we can call AB the "polynomial GCD of X and Y". Let's write the below code in the form and check the output.

```
gcd x**2-1, x**3-1
```

The calculator shows `x-1`

.

In fact, x-1 can divide both polynomials. Note that the calculator can't recognize the implicit multiplication like `2x`

, `3x`

and caret symbol `^`

. Multiplication symbol is one asterisk and power symbol is double asterisks. To calculate a polynomial GCD, all polynomials you input need separated by comma. The below won't work because the arguments are separated by space.

```
gcd x**2-1 x**3-1
```

## Auto simplification

The next example works because cos(0) is simplified to 1 before calculating the GCD.

```
gcd x-1, x-cos(0)
```

The output is `x-1`

.