Long division is a way of finding out how many times one number "goes into" another. The first number is called the divisor and the second is called the dividend. We divide to find out how many times a divisor "goes into" a dividend, that is, how many times you have to add that divisor to 0 to get the dividend. The result is the quotient, the number of times. You could guess how much, then check, but this would be slow and clumsy. The algorithm does it with a lot less guessing.

A typical problem starts like this:      divisor dividend

An algorithm is a step-by-step procedure for solving a problem

Step 1: compare the divisor, 3 with the first digit of the quotient, 5. If it is less, 3 will go into 5 at least once. In fact we guess 1.	Guess 1, put over 5 the quotient goes on top
Step 2: Multiply our guess by the divisor. Put the product under what we just divided into.	1 times 3 is 3
Step 3: Subtract from the digit(s) we just divided into	subtract 3 from 5
Step 4: Check the remainder is less than the divisor
Step 5: Bring down another digit and do it again from step 1
Step 1: guess how many times the divisor goes into the new digits. Put the guess above the digit we just brought down	3 goes into 27 about 9 times
Step 2: Multiply our guess by the divisor
Step 3: Subtract
Step 4: Check smaller than divisor
Step 5: Bring down the next digit
Step 1: Make a guess
Step 2: Multiply
Step 3: Subtract
Step 4: check remainder is smaller than divisor. Clearly, 0 is. Step 5: Bring down the next digit - can't: no more digits! We are DONE.	This is a simple example.  Try a 2 digit divisor.

The tricky part of the process is guessing.

How do you guess?

What if your guess is too low?

What if your guess is too high?

What if your guess is zero?

What if you have a remainder?

How can you check your answer?