# Get a result and calculate back to it's Divisor

In the calculation 28 /7 = 4 the result is 4 and the divisor is 7. From the result i want to calculate back into the divisor. In other words, all I have to do in this case is is 4 + 3 and i get back to the divisor 7.

But that does not work when i do 28 / 2 = 14. In this case I have to do 14 - 12 = 2 to get back to the divisor.

Is there a formula or equation that I can apply that calculates the result back to the divisor every time?

• Could you give some context please, is this for your own curiosity? Because a really quick way is to take your result and divide it from the original number to get the original divisor.
– kvmu
May 28 '13 at 6:43
• well... I feel stupid because that pretty much solves the problem I was working on. It's for a homework assignment I'm working on for class dealing with perfect numbers. May 28 '13 at 6:47
• It happens to the best of us, do not fret. :)
– kvmu
May 28 '13 at 6:49

Given a calculation of the form $P/D = Q$ (where $P$ is the original product, $D$ is the divisor, and $Q$ is the resulting quotient), you can "calculate the result back to the divisor" by using the formula $D=P/Q$.
Thus, in your first example, we have $P = 28$ and $Q=4$, so the divisor was $D=28/4=7$.
For your second example, we have $P = 28$ and $Q=14$, so the divisor was $D=28/14=2$.