What is x when 77 divided by x equals 7?

To find the answer, just divide the dividend by the quotient: 77 ÷ 7 = 11

To prove this, let's compute 77 divided by 11: $\frac{77}{11} = 7$

How does it work?

Asking what the value of x could be when 77 divided by x gives a result of 7, is equivalent to solving the following equation:

$\frac{77}{x} = 7$

Multiply both sides by x: $\frac{77 x}{x} = 7 x$
$\frac{77 x}{x}$ is equivalent to $\frac{x}{x} \times 77$ , which simplifies to $1 \times 77$ (or just $77$ ).
Thus, the equation becomes: $77 = 7 x$
To find x, divide both sides by 7: $\frac{77}{7} = \frac{7 x}{7}$
Which gives, after simplification: $11 = x$ (or $x = 11$ )

So, if the dividend is 77 and the quotient is 7, the divisor is 11.