What is x when 27 divided by x equals 6?

To find the answer, just divide the dividend by the quotient: 27 ÷ 6 = 4.5

To prove this, let's compute 27 divided by 4.5: $\frac{27}{4.5} = 6$

How does it work?

Asking what the value of x could be when 27 divided by x gives a result of 6, is equivalent to solving the following equation:

$\frac{27}{x} = 6$

Multiply both sides by x: $\frac{27 x}{x} = 6 x$
$\frac{27 x}{x}$ is equivalent to $\frac{x}{x} \times 27$ , which simplifies to $1 \times 27$ (or just $27$ ).
Thus, the equation becomes: $27 = 6 x$
To find x, divide both sides by 6: $\frac{27}{6} = \frac{6 x}{6}$
Which gives, after simplification: $4.5 = x$ (or $x = 4.5$ )

So, if the dividend is 27 and the quotient is 6, the divisor is 4.5.