Summarize:

when you divide 32 by 5, 32 is the dividend 5 is the divisor 6 is the quotient 2 is the remainder (or modulo). That will be the dividend, and the smaller the divisor. (dividend) = (divisor) * (quotient) + (remainder) Then, the 18 and 12 shift to create the third line, and the 12 and 6 shift to create the fourth line. The 3, 1, 1, and 2 that follow the multiplication symbol do not reappear. They represent how many times the divisor goes into the dividend, so they are unique to each line.
Drop any negative signs. Know your vocabulary: Identify the larger of the two numbers. Write out this algorithm: Put the larger number in the spot for dividend, and the smaller number as the divisor. Decide how many times the smaller number will divide into the larger number, and drop it into the algorithm as the quotient. Calculate the remainder, and substitute it into the appropriate place in the algorithm. Write out the algorithm again, but this time A) use the old divisor as the new dividend and B) use the remainder as the new divisor. Repeat the previous step until the remainder is zero. The last divisor is the greatest common divisor. Here is an example, where we are trying to find the GCD of 108 and 30: Notice how the 30 and the 18 in the first line shift positions to create the second line.