What is x when 100 divided by x equals 6?

To find the answer, just divide the dividend by the quotient: 100 ÷ 6 = 16.666666666667

To prove this, let's compute 100 divided by 16.666666666667: $\frac{100}{16.666666666667} = 6$

How does it work?

Asking what the value of x could be when 100 divided by x gives a result of 6, is equivalent to solving the following equation:

$\frac{100}{x} = 6$

Multiply both sides by x: $\frac{100 x}{x} = 6 x$
$\frac{100 x}{x}$ is equivalent to $\frac{x}{x} \times 100$ , which simplifies to $1 \times 100$ (or just $100$ ).
Thus, the equation becomes: $100 = 6 x$
To find x, divide both sides by 6: $\frac{100}{6} = \frac{6 x}{6}$
Which gives, after simplification: $16.666666666667 = x$ (or $x = 16.666666666667$ )

So, if the dividend is 100 and the quotient is 6, the divisor is 16.666666666667.