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.

In other words, multiples of the smaller number r < sub > k − 1 </ sub > are subtracted from the larger number r < sub > k − 2 </ sub > until the remainder is smaller than the r < sub > k − 1 </ sub >.

In the remainder of the season, Excelsior upset some of the larger league teams at home, winning against AZ and getting draws against Groningen and eventual league champions Ajax.

Depending on their success in marketing, small producers may sell a larger or smaller proportion of their product to individual buyers, wine dealers, bars and restaurants, the remainder being acquired by larger cognac houses for blending.

On May 19, 2008 a large part of the former Prince of Wales-Outer Ketchikan Census Area was annexed, including the remainder of Misty Fjords National Monument that was not already in the borough, making the current figures much larger than these.

Usually swim in a pod of a maximum of from six to twelve individuals led by a male up to 9m long who will be about 25 % larger than the females and juveniles who make up the remainder of the pod.

The municipal borough was abolished in 1974 and its former area was combined with most of the remainder of the rural district to form the larger Borough of Chelmsford.

Edward VII had the Cullinan I and Cullinan II set respectively into the Sceptre with the Cross and the Imperial State Crown, while the remainder of the seven larger stones and the 96 smaller brilliants remained in the possession of the Dutch diamond cutting firm of Messers I. J. Asscher of Amsterdam who had split and cut the Cullinan, until the South African Government bought these stones and the High Commissioner of the Union of South Africa presented them to Queen Mary on June 28, 1910.

The remainder were reorganised as the Office of the Duke of Edinburgh, with Browning as treasurer, the head of the office, moving into a new and larger office at Buckingham Palace.

If either p < sub > n </ sub ># + 1 or p < sub > n </ sub ># − 1 is a primorial prime, it means that there are larger primes than the nth prime ( if neither is a prime, that also proves the infinitude of primes, but less directly ; note that each of these two numbers has a remainder of either p − 1 or 1 when divided by any of the first n primes, and hence cannot be a multiple of any of them ).

This method strongly favours larger parties ( often smaller parties get no remainder seats, whereas the three largest parties get two each ).

The remainder goes largely to the larger cities in the UK that have adopted the PCO's London Conditions of Fitness ( including Glasgow, Edinburgh, Liverpool, Manchester, Birmingham, Coventry and Bristol ).

Nelson was debilitated by disease and had to recover before being promoted to a larger vessel, and Collingwood succeeded him in command of the Hinchinbrook and brought the remainder of the expedition back to Jamaica.

The rim of Klein has been worn and incised by a history of impacts, and the western rim is larger than the remainder.

The cartridge is said to be rimmed when the rim is of larger diameter than the remainder of the case.

Compared to some similar methods, the use of the Hare quota with the largest remainder method tends to favour the smaller parties at the expense of the larger ones.

In the Franco-Prussian War the Prussian Army, knowing that they could field substantially larger forces than the French, devised a war plan that relied on speed by encircling and destroying / bypassing French strongpoints-the Kesselschlacht or " cauldron battle "-while the remainder of the Prussian army advanced unopposed to seize important objectives such as Paris.

Larger commercial placer mining operations employ screening plants, or trommels, to remove the larger alluvial materials such as boulders and gravel, before concentrating the remainder in a sluice box or jig plant.

This subfamily is larger than all mammal families except the Cricetidae and Muridae, and is larger than all mammal orders except the bats and the remainder of the rodents.

More than half of the forty-one censured propositions come from the 95 Theses or the Resolutiones ; the larger part of the remainder are derived from the Leipzig debate.

The larger part is owned by the Englefield Estate and the remainder by West Berkshire Council.

Santa Fe traded a larger number of lower-powered locomotives for the banned passenger SDP40s, on a horsepower-for-horsepower basis, replaced the hollow bolsters with conventional HT-C bolsters, removed the water tanks ( replaced these with concrete ballast ) and eliminated the fuel / water tank in favor of an all-fuel tank and it utilized these as SDP40Fs in freight revenue service until their economic lifetime had been reached, after which they were stripped of usable service parts and the remainder of each were scrapped.

As for the remainder of Jedwabne ’ s population, IPN deplored “ the passive behavior of the majority of the town ’ s population in the face of the crime .”

Many of the others-led by Cornelis van de Heij, a farmer from Zeeland, and Father Godthard-left to form the village of Holland ( usually referred to locally as “ Hollandtown ”) rather than buying the remainder of Father Van den Broek ’ s land.

It records that the “ dynasty of Chaldea was terminated ” ( with Nabû-šuma-iškun ) and “ its kingship was transferred ,” but the remainder is lost.

Krauss originally included Tanacross with Lower Tanana, but after a more extensive linguistic survey of the region in the 1960s, he began using the term “ Transitional Tanana ”, recognizing the distinction between Tanacross and the remainder of Tanana ( Krauss, p. c .).

In an attempt to revive and spread the Local Churches, Witness Lee spent from 1984 through the remainder of his life defining and establishing “ the new way ” due to the perceived degradation and oldness that had crept into the Local Churches.

In 1611 Galileo was informed by a friend, Cigoli, “ ill-disposed men envious of your virtue and merits metdiscuss ... for any means by which they could damage you .” The number of scholars who disapproved with his Discourse on Floating Bodies, or were simply ill-spirited toward Galileo grew, but other than one letter from Niccolo Lorini there was not much discussion about the issue for the remainder of the year.

Under the premise “ First reduce what you can, then offset the remainder ”, offsetting can be done by supporting a responsible carbon project, or by buying carbon offsets or carbon credits.

* Marie Mauron: “ It is it whom one sees of the sea, first and last on his top very of light hemmed of blue, dominating its Greek Provence which knows or does not know any more that it is it, but the remainder.

The remainder was “ specially to provide for the free maintenance, education and training of choirboys, primarily those in service of the Cathedral .” This bequest founded the prestigious boys ’ school that today is called St. Albans School, which opened in October 1909.

After completing a policy review, the USCIS clarified that individuals who spent more than one year outside of U. S. and did not exhaust their entire six year term can choose to be re-admitted for the “ remainder ” of initial six-year period without being subject to the H-1B cap.

Freud regards this last source as “ perhaps more painful to us than any other ”, and the remainder of this book will extrapolate on the conflict between individual instinctual gratification-seeking and the reality of societal life.

Eventually the City of London Corporation was persuaded to take on the landowners and “ secure for the People, for the purposes of public health and recreation ” the remainder of the forest of Epping.

He writes, “ To believe your own thought, to believe that what is true for you in your private heart is true for all men, — that is genius .” The remainder of this section is spent exploring this concept.

Dugdale wrote, “ It is reported by credible tradition of this John Lord Dudley, that being a man of weak understanding, whereby he had exposed himself to some wants, and so became entangled in the usurer ’ s bonds, John Dudley, then Viscount Lisle and Earl of Warwick ( afterwards Duke of Northumberland ), thirsting after Dudley Castle, the chief seat of the family, made those money merchants his instruments to work him out of it, which by some mortgage being at length effected, this poor lord became exposed to the charity of his friends for a subsistence, and spending the remainder of his life in visits amongst them, was commonly called the Lord Quondam .”

In the process of “ collecting ” several mountain gorillas, Akeley ’ s attitude was fundamentally changed and for the remainder of his life he worked for the establishment of a gorilla preserve in the Virungas.

After re-convening, the board recommended to President Miles of the university that the students “ be separated forthwith from the University .” The President instead suspended the students for the remainder of the current semester and the next semester with leave to apply for readmission in the following year.

Apheresis ( ἀφαίρεσις ( aphairesis, “ a taking away ”)) is a medical technology in which the blood of a donor or patient is passed through an apparatus that separates out one particular constituent and returns the remainder to the circulation.

The spirits of Werner Heisenberg, Niels Bohr and Bohr ’ s wife Margrethe, meet after their deaths to attempt to answer the question which Margrethe poses in the first line of the play, “ Why did he come to Copenhagen ?” They spend the remainder of the two-act drama presenting, debating and rejecting theories that may answer that question.

Cassidy put it, “ The raging Highlanders cleared the remainder of that town as no town has been cleared for centuries, we venture to say .” One German source estimates that 300 of 355 houses were totally destroyed, for a percentage rate of 84. 5.

In 1849, Foyn married Magdalene Margrethe “ Lena ” Bull, with whom he would be married for the remainder of his life.

However, if a suited straight ( a “ lock ”) is played, any subsequently played straights must also be suited for the remainder of the round.

“ Go on strike and refuse to pay taxes ?” And much of the remainder of the book is devoted to people who decided to do just that, like Dr. A. J.

Therefore, it was necessary to make the China and India Employment Second preference category “ Unavailable ” in early April, and it will remain so for the remainder of FY-2012.