What is x when 61 divided by x equals 6?

To find the answer, just divide the dividend by the quotient: 61 ÷ 6 = 10.166666666667

To prove this, let's compute 61 divided by 10.166666666667: $\frac{61}{10.166666666667} = 6$

How does it work?

Asking what the value of x could be when 61 divided by x gives a result of 6, is equivalent to solving the following equation:

$\frac{61}{x} = 6$

Multiply both sides by x: $\frac{61 x}{x} = 6 x$
$\frac{61 x}{x}$ is equivalent to $\frac{x}{x} \times 61$ , which simplifies to $1 \times 61$ (or just $61$ ).
Thus, the equation becomes: $61 = 6 x$
To find x, divide both sides by 6: $\frac{61}{6} = \frac{6 x}{6}$
Which gives, after simplification: $10.166666666667 = x$ (or $x = 10.166666666667$ )

So, if the dividend is 61 and the quotient is 6, the divisor is 10.166666666667.