What is x when 61 divided by x equals 8?

To find the answer, just divide the dividend by the quotient: 61 ÷ 8 = 7.625

To prove this, let's compute 61 divided by 7.625: $\frac{61}{7.625} = 8$

How does it work?

Asking what the value of x could be when 61 divided by x gives a result of 8, is equivalent to solving the following equation:

$\frac{61}{x} = 8$

Multiply both sides by x: $\frac{61 x}{x} = 8 x$
$\frac{61 x}{x}$ is equivalent to $\frac{x}{x} \times 61$ , which simplifies to $1 \times 61$ (or just $61$ ).
Thus, the equation becomes: $61 = 8 x$
To find x, divide both sides by 8: $\frac{61}{8} = \frac{8 x}{8}$
Which gives, after simplification: $7.625 = x$ (or $x = 7.625$ )

So, if the dividend is 61 and the quotient is 8, the divisor is 7.625.