How to Find the Greatest Common Divisor of Two Integers

Step-by-Step Guide

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   Step 1: Drop any negative signs.

   That will be the dividend, and the smaller the divisor. ,,,,,,,,, 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.
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   Step 2: Know your vocabulary: when you divide 32 by 5

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   Step 3: 32 is the dividend 5 is the divisor 6 is the quotient 2 is the remainder(or modulo).

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   Step 4: Identify the larger of the two numbers.

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   Step 5: Write out this algorithm: (dividend) = (divisor) * (quotient) + (remainder)

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   Step 6: Put the larger number in the spot for dividend

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   Step 7: and the smaller number as the divisor.

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   Step 8: Decide how many times the smaller number will divide into the larger number

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   Step 9: and drop it into the algorithm as the quotient.

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    Step 10: Calculate the remainder

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    Step 11: and substitute it into the appropriate place in the algorithm.

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    Step 12: Write out the algorithm again

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    Step 13: but this time A) use the old divisor as the new dividend and B) use the remainder as the new divisor.

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    Step 14: Repeat the previous step until the remainder is zero.

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    Step 15: The last divisor is the greatest common divisor.

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    Step 16: Here is an example

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    Step 17: where we are trying to find the GCD of 108 and 30:

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    Step 18: Notice how the 30 and the 18 in the first line shift positions to create the second line.

Detailed Guide

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