Did you ever realize that long division is the reverse operation of multiplication?

I have been tutoring an adult in arithmetic. In the process I noticed something that I never noticed before. It now seems so obvious.

Let me explain. Imagine multiplying two numbers. Let’s say that the bottom number has 3 digits. Going from right to left, you multiply each of the three digits with the top number. Then you add the three lines.

Now imagine dividing top number into the answer you got from the multiplication. Going from left to right (reverse of right to left), you produce each of the three digits of the bottom number, multiply and subtract (reverse of adding). Each line that you subtract is exactly the same as the corresponding line from the multiplication. When adding the lines in the multiplication, you go from zero (in a sense) to the product of the two numbers. When dividing, you subtract from the product to eventually get zero.

I have not gotten around yet to teaching division. I wonder if pointing out the above observation would be useful for teaching it.