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Topic: Divisible

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	Divisor - Wikipedia, the free encyclopedia
		Numbers divisible by 2 are called even and those that are not are called odd.
		The name comes from the arithmetic operation of division: if a/b = c then a is the dividend, b the divisor, and c the quotient.
		This lattice is isomorphic to the dual of the lattice of subgroups of the infinite cyclic group Z.
	en.wikipedia.org /wiki/Divisor (627 words)

	Divisibility
		Divisibility Test for 3: if the sum of the digits of a number is divisible by 3, then the number is divisible by 3.
		150 is not divisible by 9 since the sum of the digits is 6, and 6 is not divisible by 9.
		91 is not evenly divisible by 4 (remainder is 3).
	www.mathgoodies.com /lessons/vol3/divisibility.html (1549 words)

	PlanetMath: divisibility in rings
		Divisibility is a reflexive and transitive relation in
		See Also: prime element, irreducible, group of units, divisibility by prime number, gcd domain, corollary of Bézout's lemma, unity plus nilpotent is unit
		This is version 10 of divisibility in rings, born on 2004-10-08, modified 2006-06-24.
	planetmath.org /encyclopedia/Divisible.html (89 words)

	Whole Numbers and Their Basic Properties
		The number 714558 is divisible by 6, since its units digit is even, and the sum of its digits is 30, which is divisible by 3.
		The number 724560 is divisible by 12, since the number formed by its last two digits, 60, is divisible by 4, and the sum of its digits is 30, which is divisible by 3.
		A number is divisible by 25 if the number formed by the last two digits is any of 0, 25, 50, or 75 (the number formed by its last two digits is divisible by 25).
	www.mathleague.com /help/wholenumbers/wholenumbers.htm (2880 words)

	technocosm.org - Divisibility of Whole Numbers
		Since 52a is evenly divisible by 5, then only b needs to be evenly divisible by 5, which means b must be 5 or 0.
		A number is evenly divisible by 11 the alternating sum of its digits are divisible by 11 (including zero).
		A number is evenly divisible by 13 if, when you delete the last digit from the given number, then subtract nine times the deleted digit from the remaining number, what is left is divisible by 13, then so is the original number.
	www.technocosm.org /chaos/divisibility.html (1122 words)

	Divisible group - Wikipedia, the free encyclopedia
		In group theory, a divisible group is an abelian group G such that for any positive integer n and any g in G, there exists y in G such that ny = g.
		One can show that G is divisible if and only if G is an injective object in the category of abelian groups.
		Since a divisible group is an injective module, Tor(G) is a direct summand of G.
	en.wikipedia.org /wiki/Divisible_group (285 words)

	PlanetMath: divisible group
		Every group is isomorphic to a subgroup of a divisible group.
		Any divisible abelian group is isomorphic to the direct sum of its torsion subgroup and
		This is version 4 of divisible group, born on 2003-07-23, modified 2003-07-24.
	planetmath.org /encyclopedia/DivisibleGroup.html (95 words)

	The Internet Classics Archive \| Physics by Aristotle
		Moreover, it is plain that everything continuous is divisible into divisibles that are infinitely divisible: for if it were divisible into indivisibles, we should have an indivisible in contact with an indivisible, since the extremities of things that are continuous with one another are one and are in contact.
		The same reasoning will show the divisibility of the length, and in fact of everything that forms a sphere of change (though some of these are only accidentally divisible because that which changes is so): for the division of one term will involve the division of all.
		And we now see that in most cases the fact that all the terms are divisible or infinite is a direct consequence of the fact that the thing that changes is divisible or infinite: for the attributes 'divisible' and 'infinite' belong in the first instance to the thing that changes.
	classics.mit.edu /Aristotle/physics.6.vi.html (7134 words)

	Problem E - Math & Number Theory Lovers' Contest
		In decimal number system a number is divisible by 4 if the number formed by rightmost two digits is divisible by 4.
		A number is divisible by 11 if the difference of the sums of its odd positioned digits and even positioned digits from the right is divisible by 11.
		A number is divisible by 7 if the difference of the sums of the summation of the numbers formed by alternate three digits from the right is divisible by 7.
	acm.uva.es /p/v102/10211.html (516 words)

	Divisibility Rules
		use divisibility rules to determine if a number is divisible by 2, 3, 4, 5, 6, 9, or 10.
		To find out if a number is divisible by seven, take the last digit, double it, and subtract it from the rest of the number.
		Since 36, is divisible by both 2 and 3, it is also divisible by 6.
	argyll.epsb.ca /jreed/math7/strand1/1104.htm (396 words)

	divisibility.html
		2.1732782989264864826421834612 is divisible by four also, because 12 is divisible by 4.
		If the number is divisible by both 3 and 2 (even), it is divisible by 6 as well.
		To find out if a number is divisible by 7, take the last digit, double it, and subtract it from the rest of the number.
	www.pvpusd.k12.ca.us /teachweb/weitzs/divisibility.html (350 words)

	Math Lair - Divisibility Tests (Site not responding. Last check: 2007-11-03)
		One interesting way of passing time is to try and figure out whether some large number is divisible by some smaller number (which is another way of saying that the large number is congruent to 0 modulo the smaller number).
		For example, 284,691 is divisible by 3 because its digits sum to 2+8+4+6+9+1 = 30, and 30 is a multiple of 3.
		The smallest number divisible by every number between 2 and 12 is 27,720, so try this number out to see whether you can get all of the tests to work.
	www.stormloader.com /ajy/divisible.html (630 words)

	Division by 81
		For those who remember the rules that a number is divisible by 3 and 9 if and only if (iff) the sum of its digits is divisible by 3 or 9, respectively, it's tempting to assume that the same applies to 81.
		That is a number is divisible by 81 iff the sum of its digits is divisible by 81.
		Therefore the number in parenthesis is divided by 9 and hence N is divisible by 81.
	www.cut-the-knot.org /Generalization/81.shtml (572 words)

	Math Forum: Calculation Tips & Tricks
		So, to continue the last example, 33333888 is divisible by 8 because the digit in the hundreds place is an even number, and the last two digits are 88, which is divisible by 8.
		33333886 is not divisible by 8 because the digit in the hundreds place is an even number, but the last two digits are 86, which is not divisible by 8.
		First we want to find whether it is divisible by 11, but on the way we are going to save the numbers that we use: in every step we will subtract the last digit from the other digits, then save the subtracted amount in order.
	mathforum.org /k12/mathtips/division.tips.html (2423 words)

	Puzzle 101. Digital Divisibility Tests
		Division by 2 or 5 is done merely by looking at the last digit, since 2 and 5 are factors of the base 10.
		Division rules exist with multiplier k if 10k-1 is divisible by p.
		Since 10^(p-1)-1 is divisible by p, a general division rule for p is take the last p-1 digits, and add to the rest.
	www.primepuzzles.net /puzzles/puzz_101.htm (2058 words)

	Math Forum: Explaining the Divisibility Rules
		Therefore, the whole number is divisible by 9 and the quotient is 137.
		Therefore, the whole number is divisible by 11 and the quotient is 11,223,302.
		Also, if a number is divisible by both 3 and 2, then the whole number is divisible by 6.
	mathforum.org /k12/mathtips/ward.html (826 words)

	Insolvency - Divisible Property in Bankruptcy
		The Bankruptcy Act separates "divisible" assets (those assets that are available to the trustee) from "non-divisible" assets (those assets that are not available to the trustee).
		It is easiest to initially think of divisible property as all of the property of the bankrupt and work backwards from there.
		is property divisible amongst the creditors of the bankrupt.
	www.worrells.net.au /Community/insolvency/divisible_property.htm (3114 words)

	Divisible Property (Site not responding. Last check: 2007-11-03)
		This new type of property is called "divisible property." To understand why the legislature thought it necessary to add a new type of property, it is important to understand that the date for valuation of marital property in North Carolina is a couple's date of separation.
		All appreciation and diminution in value of marital property and divisible property of a couple occurring after the date of separation and prior to the date of distribution, except that appreciation or diminution in value which is the result of postseparation actions or activities of a spouse shall not be treated as divisible property.
		For example, previously in divorce planning a lawyer might have advised a client who planned to separate to instruct or request of his employer that he or she not be paid a bonus until after his or her date of separation from his spouse.
	www.bsp-pa.com /Xbspdiv.stm (601 words)

	Criteria of divisibility by 9 and 11
		The alternating sum of digits is 2-0+0-0+2=4 and is divisible by 4.
		Then, for example, 511 is divisible by 7.
		As a result, 1302 is divisible by 7.
	www.cut-the-knot.org /Generalization/div11.shtml (284 words)

	[No title] (Site not responding. Last check: 2007-11-03)
		A: Yes, because the rule is: in the Gregorian calendar, leap years occur in years exactly divisible by four, except that years ending in 00 are leap years only if they are divisible by 400.
		A: No, 'tis too, because the rule is: in the Gregorian calendar, leap years occur in years exactly divisible by four, except that years ending in 00 are leap years only if they are divisible by 400.
		A: Some of them aren't, but 2000 is, because the rule is: in the Gregorian calendar, leap years occur in years exactly divisible by four, except that years ending in 00 are leap years only if they are divisible by 400.
	world.std.com /~dpbsmith/leapyearfaq.txt (1218 words)

	Taxes
		When the difference--the amount you are out of balance or off from the expected total--is evenly divisible by 9, you have a transposition error.
		No, 17,520 is not evenly divisible by 9.
		It is divisible by 9, as all transposition differences are.
	taxes.scriptmania.com (735 words)

	Numbers Divisible by 6
		Even numbers are always evenly divisible by 2.
		Numbers are evenly divisible by 3 if the sum of all the individual digits is evenly divisible by 3.
		For example, the sum of the digits for the number 3627 is 18, which is evenly divisible by 3 but 3627 is an odd number so the number 3627 is not evenly divisible by 6.
	www.aaamath.com /div66-divisibility6.html (108 words)

	Hector Parr's Essays: Conditionals and Counterfactuals
		(16 is divisible be 2) IMPLIES (16 is divisible by 3) is FALSE
		With the possible exception of the third row, this is all nonsense.
		It is not because 18 is divisible be 2 that it also divides by 3.
	www.c-parr.freeserve.co.uk /hcp/if.htm (4266 words)

	divisible - OneLook Dictionary Search
		divisible : The American Heritage® Dictionary of the English Language [home, info]
		Divisible : Eric Weisstein's World of Mathematics [home, info]
		Phrases that include divisible: divisible group, divisible module, divisible contract clause, divisible property, infinitely divisible, more...
	www.onelook.com /?w=divisible (188 words)

	Calendar Converter
		Whatever the problems of Y2K, they won't include sloppy programming which assumes every year divisible by 4 is a leap year since 2000, unlike the previous and subsequent years divisible by 100, is a leap year.
		By the time the 1900 blunder was discovered, Excel users had created millions of spreadsheets containing incorrect day numbers, so Microsoft decided to leave the error in place rather than force users to convert their spreadsheets, and the error remains to this day.
		Note, however, that only 1900 is affected; while the first release of Excel probably also screwed up all years divisible by 100 and hence implemented a purely Julian calendar, contemporary versions do correctly count days in 2000 (which is a leap year, being divisible by 400), 2100, and subsequent end of century years.
	www.fourmilab.ch /documents/calendar (5200 words)

	Mathematics Fun, Fiction, Function, Fantasy
		To find if some number X is divisible by a certain number, test the number by using the information in the table below.
		The first sum is the sum of the first, third, fifth, seventh, etc. digits and the other sum is the sum of the second, fourth, sixth, eighth, etc. digits.
		You can use multiple rules for multiple divisors...for instance, to check if a number is divisible by 57, check to see if it is divisible by 19 and 3, etc., since 57 = 19 x 3...
	www.lifesmith.com /mathfun.html (5533 words)

	Freeware Palm: Divisible v1.04
		Divisible asks students if a random number is divible by either 1, 2, 3, 4, 5, 6, 9, or 10.
		If answered incorrectly, Divisible displays the divisiblity rule.
		FreewarePalm.com is not affiliated with or endorsed by Palm, Inc., palmOne or PalmSource in any way.
	www.freewarepalm.com /educational/divisible.shtml (76 words)

	divisible (Site not responding. Last check: 2007-11-03)
		Recognition of Prime Numbers Game - a web page that permits one to test knowledge of the primes and composites from 1 through 100
		Divisibility Tests - 2 through 10 with links to other resources
		State a number which is divisible by 15 and also is divisible by 7 and also is divisible by 2.
	www.mathnstuff.com /math/spoken/here/1words/d/d33.htm (175 words)

	[No title]
		NORTHBOUND GVW WEIGHT TABLE 2 FOR DIVISIBLE LOADS 34,000 POUNDS, TANDEM AXLE 105,500 POUNDS.
		NORTHBOUND IS RESTRICTED TO GVW WEIGHT TABLE 2 FOR DIVISIBLE LOADS 34,000 POUNDS, TANDEM AXLE 105,500 POUNDS.
		SOUTHBOUND COAST FORK WILLAMETTE RIVER BRIDGE RESTRICTED TO GVW WEIGHT TABLE 2 FOR DIVISIBLE LOADS AND GVW WEIGHT TABLE 3 FOR NON-DIVISIBLE LOADS.
	www.tripcheck.com /reports/odotosp2.txt (275 words)

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