What is x when 71 divided by x equals 66?

To find the answer, just divide the dividend by the quotient: 71 ÷ 66 = 1.0757575757576

To prove this, let's compute 71 divided by 1.0757575757576: $\frac{71}{1.0757575757576} = 66$

How does it work?

Asking what the value of x could be when 71 divided by x gives a result of 66, is equivalent to solving the following equation:

$\frac{71}{x} = 66$

Multiply both sides by x: $\frac{71 x}{x} = 66 x$
$\frac{71 x}{x}$ is equivalent to $\frac{x}{x} \times 71$ , which simplifies to $1 \times 71$ (or just $71$ ).
Thus, the equation becomes: $71 = 66 x$
To find x, divide both sides by 66: $\frac{71}{66} = \frac{66 x}{66}$
Which gives, after simplification: $1.0757575757576 = x$ (or $x = 1.0757575757576$ )

So, if the dividend is 71 and the quotient is 66, the divisor is 1.0757575757576.