For example, the subprogram in Euclid's algorithm to compute the remainder would execute much faster if the programmer had a " modulus " ( division ) instruction available rather than just subtraction ( or worse: just Minsky's " decrement ").

And to " measure " is to place a shorter measuring length s successively ( q times ) along longer length l until the remaining portion r is less than the shorter length s. In modern words, remainder r = l − q * s, q being the quotient, or remainder r is the " modulus ", the integer-fractional part left over after the division.

Doubleday was humiliated by this snub and held a lasting grudge against Meade, but he returned to division command and fought well for the remainder of the battle.

Bézout's lemma is a consequence of the Euclidean division defining property, namely that the division by a nonzero integer b has a remainder strictly less than | b |.

A passage in Muhtasar kitab al-buldan illustrates the division of Islamic society into strata: " First are the rulers, whom their deserts has placed in the foremost rank ; second are the viziers, distinguished by wisdom and understanding ; third are the wealthy upper classes, lifted by their possessions ; fourth are the middle classes who are attached to the upper three by culture ( ta ' addub ); the remainder are the lowest classes that are filthy refuse, a torrent of scum, none of whom thinks of anything but food and sleep.

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.

In the same manner, the remainder of the division indicates the year in the Metonic cycle ( years 1 to 18 ) the year is in.

We can allow the table size n to not be a power of 2 and still not have to perform any remainder or division operation, as these computations are sometimes costly.

In that case, if n is 10000 or so, the division formula ( z × n ) ÷ N, which depends mainly on the leading digits, will generate a lot of collisions ; whereas the remainder formula z mod n, which is quite sensitive to the trailing digits, may still yield a fairly even distribution.

Then the remainder of on division by is 5.

As a consequence of the polynomial remainder theorem, the entries in the third row are the coefficients of the second-degree polynomial, the quotient of on division by.

The notion of modular arithmetic is related to that of the remainder in division.

While the Brewers were still holding on to the Wild Card lead, the division was never seriously challenged for the remainder of the year.

#: Is set to the remainder of integer division.

* Modulo operation, in computing, the remainder after division

The polynomials q and r are uniquely determined by f and g. This is called Euclidean division, division with remainder or polynomial long division and shows that the ring F is a Euclidean domain.

The strike prematurely ended what could have been the Rangers ' first division championship when commissioner Bud Selig canceled the remainder of the season and the playoffs.

The Julian day number can be calculated using the following formulas ( integer division is used exclusively, that is, the remainder of all divisions are dropped ):

Blocks of data entering these systems get a short check value attached, based on the remainder of a polynomial division of their contents ; on retrieval the calculation is repeated, and corrective action can be taken against presumed data corruption if the check values do not match.

This polynomial resembles the divisor in a polynomial long division, which takes the message as the dividend and in which the quotient is discarded and the remainder becomes the result, with the important distinction that the polynomial coefficients are calculated according to the carry-less arithmetic of a finite field.

Similar to the view of Leopold Kronecker that " God made the integers ; all else is the work of man ," musicians drawn to the alphorn and other instruments that sound the natural harmonics, such as the natural horn, consider the notes of the natural harmonic series — particularly the 7th and 11th harmonics — to be God's Notes, the remainder of the chromatic scale enabled by keys, valves, slides and other methods of changing the qualities of the simple open pipe being an artifact of mere mortals.

The remainder of the first of the two Cathar wars now essentially focused on Simon's attempt to hold on to his fabulous gains through winters where he was faced, with only a small force of confederates operating from the main winter camp at Fanjeau, with the desertion of local lords who had sworn fealty to him out of necessity — and attempts to enlarge his newfound domains in the summer when his forces were greatly augmented by reinforcements from northern France, Germany and elsewhere.

The core band that coalesced around this album and tour — rhythm guitarist Alomar, bassist George Murray, and drummer Dennis Davis — would continue as a stable unit for the remainder of the 1970s.

Genesis appears to be structured around the recurring phrase elleh toledot, meaning " these are the generations ," with the first use of the phrase referring to the " generations of heaven and earth " and the remainder marking individuals — Noah, the " sons of Noah ", Shem, etc., down to Jacob.

The remainder of Abbadie's life was spent in writing and preaching, and in the performance — not too sedulous, for he was frequently absent from his benefice — of the ordinary duties of his office, varied by visits to England and to Holland, where most of his books were printed.

Although he was short of money, Saladin also allowed the departing Zangi to take all the stores of the citadel that he could travel with and to sell the remainder — which Saladin purchased himself.

* 25 November 1875 — Britain becomes a minority share holder in the Suez Company, acquiring 44 % of the Suez Canal Company, with the remainder being controlled by French business syndicates.

For the remainder of the 19th century, under a series of elected and appointed presidents, Uruguay saw interventions by — and conflicts with — neighboring states, political and economic fluctuations, and large inflows of immigrants, mostly from Europe.

The typical grain mixture for bourbon, known as the mash bill, is 70 % corn — with the remainder being wheat, rye, and / or malted barley.

The remainder of the Dasyuridae are referred to as ' marsupial mice '; most weigh less than 100 g. There are two species of Marsupial Mole — order Notoryctemorphia — that inhabit the deserts of Western Australia.

In such cases the winner of the bout typically receives around 30, 000 yen net per sponsor ( out of the sponsors contribution of 60, 000 yen — much of the remainder goes in paying the wrestler's tax on the prize ).

The cause of the Stuarts now lost, the remainder of his life was — with a brief exception — spent in exile.

Yair Chayim Bacharach ( 1639, Lipník nad Bečvou, Moravia — 1702 ) was a German rabbi and major 17th century posek, who lived first in Koblenz and then remainder of his life in Worms and Metz.

And Davis ' signing coincided with an injury to Jermaine O ' Neal that would knock him out for virtually the remainder of the regular season — indeed, O ' Neal's first missed game due to his injury was Davis ' first game back with the Pacers.

The Joint Committee's Strabane — Derry line was closed in 1954, followed by the remainder of the narrow gauge system in 1960.

Three specific targets of satire — racism, the President of the United States, and the Vietnam War — would wind up defining the show's content for the remainder of its run, and eventually lead to its demise.

There were two religious classes in the place — that in the south part was the Scotch-Irish stock and favored Presbyterianism, while the remainder were Congregationalists.

At this point, Christian V no longer had his most experienced foreign relations counsel around to repair the political damage — in 1676 he had been persuaded to sacrifice Griffenfeldt as a traitor, and to the clamour of his adversaries, Griffenfeldt was imprisoned for the remainder of his life.

As a result, the elite 4th Airborne Infantry Brigade that had received orders to deploy to assist operations in Tucumán province would remain stationed in the capital Córdoba province for the remainder of the year.

The remainder served in segregated combat units, most notably the 24th Infantry Regiment.

Additional German reinforcements began arriving and by late evening portions of the 111th Infantry Division occupied the third line near Acheville and Arleux, with the remainder of the division arriving the following day.

Troop A attached 5 February 1908 to the 1st Regiment of Infantry ( see below ); remainder of squadron concurrently disbanded.

Trenchard spent the remainder of 1901 on patrolling duties, and in early 1902 he was appointed acting commander of the 23rd Mounted Infantry Regiment.

In 1862, Gunn enlisted in the 27th Wisconsin Infantry, and served with them for the remainder of the war.

The petition was promptly granted, and Adolf Hitler thereupon joined the Bavarian Army, eventually settling into the 16th Reserve Bavarian Infantry Regiment, where he served the remainder of the war.

At the time, the division had a strength of 8, 500 out of the 16, 000 planned, so the military transferred troops from the 30th, 31st, and 33rd Infantry Division to fill out the remainder of the division.

Of the total number, 20, 300 were Imperial Japanese Army troops of the 5th Infantry Division under Lt. General Yamaguchi Motoomi, the remainder were 540 naval rikusentai from the Imperial Japanese Navy.

He served in France from 1914 as a lieutenant in the 10th Service Battalion-Somerset Light Infantry and the Honourable Artillery Company, but was severely wounded at Cambrai the following year, with eleven bullets in his left leg, and spent most of the remainder of the war in a wheelchair.

The 15th and 16th were assigned to the 34th Division and the 17th to the 35th Infantry Division, moved to France in early 1916, and first saw action at the first day on the Somme ; all three spent the remainder of the war on the Western Front.

The three regiments of the 66th Infantry Division arrived in England, 26 November 1944, and the remainder of the Division, 12 December 1944, training until 24 December 1944 when the Division crossed the English Channel to Cherbourg on two Belgian steamships, the Chesire and the Leopoldville.

The division's 422nd and 423rd Infantry Regiments were encircled and cut off from the remainder of the Division by a junction of enemy forces in the vicinity of Schonberg.

The remainder ( 4th, 14th, 17th, 26th and 27th Infantry Divisions ), which didn't manage to cross the river, with General Bortnowski, capitulated between 18 and 22 September.

Two battalions joined the Marine Raiders on New Georgia, 5 July 1943, while the remainder of the division landed, 22 July, and assisted the 43d Infantry Division in taking Munda airfield in heavy fighting.

Meanwhile, the remainder of the division relieved the 6th Infantry Division in the Sarmi-Wakde island area, 18 July 1944, built bridges, roads, and docks, patrolled the area, and engaged small units of the enemy, trying not to provoke a large scale counterattack by the enemy.

The 32nd Battalion saw no major offensive action for the remainder of the year, and on 2 January 1917, Wark gained admission to the Army Infantry School.

He spent the remainder of 1861 in the Kanawha Valley in western Virginia in the 5th and 45th Virginia Infantry regiments.

The remainder of the 83rd Infantry and 3rd Mountain Divisions, encircled south of Velikiye Luki, fought their way west to meet the relieving troops.

Horrocks spent the remainder of the inter-war years in postings that included adjutant for the 9th Battalion, Middlesex Regiment of the Territorial Army ( 1926 — 1930 ); student at the Staff College, Camberley ( 1931 — 1932 ); Staff Captain at the War Office ( 1934 — 1936 ); Brigade Major with the 5th Infantry Brigade ( 1936 — 1938 ); and instructor at the Staff College.

Of the total number, 20, 300 were Imperial Japanese Army troops of the 5th Infantry Division under Lt. General Yamaguchi Motoomi, the remainder were 540 naval rikusentai from the Imperial Japanese Navy.

On May 6, 1945, the remainder under command of Horst Freiherr Treusch und Buttlar-Brandenfels surrendered to the 26th Infantry Division.

Four days later it reached Normandy, but for the remainder of July 1944, the 37th simply waited in reserve while the 4th Armored Division relieved elements of the weary 4th Infantry Division.

) The unit, heavily combat-attrited in Italy, was redesignated on 10 December 1943 as the 509th Parachute Infantry Battalion, a designation it retained for the remainder of the war.