What is x when 27 divided by x equals 16?

To find the answer, just divide the dividend by the quotient: 27 ÷ 16 = 1.6875

To prove this, let's compute 27 divided by 1.6875: $\frac{27}{1.6875} = 16$

How does it work?

Asking what the value of x could be when 27 divided by x gives a result of 16, is equivalent to solving the following equation:

$\frac{27}{x} = 16$

Multiply both sides by x: $\frac{27 x}{x} = 16 x$
$\frac{27 x}{x}$ is equivalent to $\frac{x}{x} \times 27$ , which simplifies to $1 \times 27$ (or just $27$ ).
Thus, the equation becomes: $27 = 16 x$
To find x, divide both sides by 16: $\frac{27}{16} = \frac{16 x}{16}$
Which gives, after simplification: $1.6875 = x$ (or $x = 1.6875$ )

So, if the dividend is 27 and the quotient is 16, the divisor is 1.6875.