What is x when 65 divided by x equals 5?

To find the answer, just divide the dividend by the quotient: 65 ÷ 5 = 13

To prove this, let's compute 65 divided by 13: $\frac{65}{13} = 5$

How does it work?

Asking what the value of x could be when 65 divided by x gives a result of 5, is equivalent to solving the following equation:

$\frac{65}{x} = 5$

Multiply both sides by x: $\frac{65 x}{x} = 5 x$
$\frac{65 x}{x}$ is equivalent to $\frac{x}{x} \times 65$ , which simplifies to $1 \times 65$ (or just $65$ ).
Thus, the equation becomes: $65 = 5 x$
To find x, divide both sides by 5: $\frac{65}{5} = \frac{5 x}{5}$
Which gives, after simplification: $13 = x$ (or $x = 13$ )

So, if the dividend is 65 and the quotient is 5, the divisor is 13.