**Description**

The simplest form of Euclid's algorithm starts with a pair of positive integers and forms a new pair that consists of the smaller number and the difference between the larger and smaller numbers. The process repeats until the numbers are equal; then that value is the greatest common divisor of the original pair. However if one number is much smaller than the other, many subtraction steps will be needed before the larger number is reduced to a value less than or equal to the other number in the pair.

Subtracting a small positive number from a big number enough times until what is left is less than the original smaller number can be replaced by finding the remainder in long division. Thus the division form of Euclid's algorithm starts with a pair of positive integers and forms a new pair that consists of the smaller number and the remainder obtained by dividing the larger number by the smaller number. The process repeats until one number is zero. The other number then is the greatest common divisor of the original pair.

Read more about this topic: Euclidean Algorithm

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### Famous quotes containing the word description:

“The type of fig leaf which each culture employs to cover its social taboos offers a twofold *description* of its morality. It reveals that certain unacknowledged behavior exists and it suggests the form that such behavior takes.”

—Freda Adler (b. 1934)

“The next Augustan age will dawn on the other side of the Atlantic. There will, perhaps, be a Thucydides at Boston, a Xenophon at New York, and, in time, a Virgil at Mexico, and a Newton at Peru. At last, some curious traveller from Lima will visit England and give a *description* of the ruins of St. Paul’s, like the editions of Balbec and Palmyra.”

—Horace Walpole (1717–1797)

“To give an accurate *description* of what has never occurred is not merely the proper occupation of the historian, but the inalienable privilege of any man of parts and culture.”

—Oscar Wilde (1854–1900)