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		The basic rule for divisibility by 4 is that if the last two digits in a number is divisible by 4, the original number is divisible by 4 (This is because 100 is divisible by 4 and so adding hundreds, thousands, etc. is simply adding another number that is divisible by 4).
		Divisibility by 6 is determined by checking the original number to see if it is both an even number (divisible by 2) and divisible by 3.
		Divisibility by 7 is the most difficult single digit number for which to define divisibility rules, but there are quite straightforward tests that work in this case.
	www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Divisibility_rule (3160 words)

	Divisibility Rules (Site not responding. Last check: 2007-10-26)
		-3 (mod 13) (i.e., 10 - -3 is divisible by 13)
		-4 (mod 13) (i.e., 100 - -4 is divisible by 13)
		-1 (mod 13) (i.e., 1000 - -1 is divisible by 13)
	www2.sunysuffolk.edu /wrightj/MA22/Num/DivRule.htm (732 words)

	PlanetMath: divisibility test
		For example, suppose that for some reason you wanted to determine whether 24709898213 is divisible by 11 but didn't have access to (or didn't want to use) a calculator or computer.
		Divisibility tests are usually more useful for humans than for computers, and then only for sufficiently small numbers.
		This is version 2 of divisibility test, born on 2006-06-13, modified 2006-06-13.
	planetmath.org /encyclopedia/DivisibilityTest.html (371 words)

	Divisibility Rules (Site not responding. Last check: 2007-10-26)
		10 = -3 (mod 13) (i.e., 10 - -3 is divisible by 13)
		100 = -4 (mod 13) (i.e., 100 - -4 is divisible by 13)
		1000 = -1 (mod 13) (i.e., 1000 - -1 is divisible by 13)
	planet.tvi.edu /jbrown/divisibility_rules.htm (888 words)

	PlanetMath: divisibility test
		For example, suppose that for some reason you wanted to determine whether 24709898213 is divisible by 11 but didn't have access to (or didn't want to use) a calculator or computer.
		Divisibility tests are usually more useful for humans than for computers, and then only for sufficiently small numbers.
		This is version 2 of divisibility test, born on 2006-06-13, modified 2006-06-13.
	www.planetmath.org /encyclopedia/DivisibilityRule.html (371 words)

	Top40-Charts.com - 40 Top 20 & Top 40 Music Charts from 25 Countries
		The basic rule for divisibility by 4 is that if the last two digits in a number is divisible by 4, the whole number is divisible by 4 (This is because 100 is divisible by 4 and so adding hundreds, thousands, etc. is simple adding another number that is divisible by 4).
		Divisibility by 6 is determined by checking the original number to see if it is both an even number (divisible by 2) and divisible by 3.
		Divisibility by 7 is the most difficult single digit number for which to define divisibility rules.
	www.top40-charts.com /pedia.php?title=Divisibility_rule (3838 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)

	Divisibility Rules (Tests)
		Divisible By "Divisible By" means "If you divide one number by another, is the result a whole number?"
		The number is divisible by both 2 and 3
		Not only are there divisibility tests for larger numbers, but there are more tests for the numbers we have shown.
	www.mathsisfun.com /divisibility-rules.html (251 words)

	Divisibility War
		In subsequent lessons it is easier for students to use their division skills to learn the new lesson rather than apply the divisibility tests- a skill they have not mastered.
		Divisibility War can fill in gaps in class time and is designed to provide immediate feedback to students as they practice using the divisibility rules.
		I also realized that the level of difficulty of Divisibility War can be reduced by omitting the challenger rule(#7) at first and having students use three or four of the divisibility tests instead of all seven to determine the winner of a round.
	edweb.sdsu.edu /courses/edtec670/Cardboard/card/d/Divisibility.html (1421 words)

	NationMaster - Encyclopedia: Divisor
		In mathematics, the result of the division of two integers usually cannot be expressed with an integer quotient, unless a remainder â€”an amount left overâ€” is also acknowledged.
		Numbers divisible by 2 are called even and numbers not divisible by 2 are called odd.
		A divisibility rule is a method that can be used to determine whether a number divides other numbers.
	www.nationmaster.com /encyclopedia/Divisor (1771 words)

	Divisibility rule - Wikipedia, the free encyclopedia
		Divisibility rules are useful when it is necessary to determine a number's factors and a calculator is not present, or if the number is too high for the calculator to compute.
		The basic rule for divisibility by 4 is that if the last two digits in a number is divisible by 4, the whole number is divisible by 4 (This is because 100 is divisible by 4 and so adding hundreds, thousands, etc. is simple adding another number that is divisible by 4).
		A number is divisible by a given divisor, if it is divisible by the highest power of each of its prime factors.
	en.wikipedia.org /wiki/Divisibility_rule (2513 words)

	Divisibility Criteria
		Divisibility criteria are ways of telling whether one number divides another without actually carrying the division through.
		Divisibility criteria re constructed in terms of the digits that compose a given number.
		Proceed with these steps until you obtain a number which is obviously divisible by 19 or is obviously not divisible by 19.
	www.cut-the-knot.org /blue/divisibility.shtml (424 words)

	Divisibility Rules
		Ex [1] 34,164 is divisible by 4 because 64 is divisible by 4.
		Ex [1] 34,164 is divisible by 6 because it is divisible by 2 and 3.
		Ex [1] 34,164 is divisible by 12 because it is divisible by 3 and 4.
	sky.prohosting.com /numsense/Basic_Memorization/Divisible.htm (720 words)

	Divisor - Art History Online Reference and Guide
		A divisibility rule is a rule you can use to determine a number's divisibility by another number.
		A number is divisible by 14 iff it's divisible by 2 and by 7.
		A number is divisible by 15 iff it's divisible by 3 and by 5.
	www.arthistoryclub.com /art_history/Divisibility_rule (875 words)

	Divisibility Rules: How to test if a number can be divided by 2,3,4,5,6,8,9 or 10. Divisibility Calculator
		Rule: A number is divisible by 5 if the its last digit is a 0 or 5.
		Since 6 is a multiple of 2 and 3, the rules for divisibility by 6 are a combination of the rule for 2 and the rule for 3.
		Rule A number is divisible by 6 if it is even and if the sum of its digits is divisible by 3.
	www.mathwarehouse.com /arithmetic/numbers/divisibility-rules-and-tests.php (2375 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)

	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)

	essay1
		This is known as the alternating summation rule for divisibility by 11.
		One version states that a number is divisible by 11 if the alternating sum of the digits is also divisible 11, meaning that the alternating sum must be a multiple of 11.
		The second version states that a number is divisible by 11 if the sum of every other digit starting with the right-most digit is equal to the sum of every other digit starting with the second digit from the right, meaning that the alternating sum is 0.
	jwilson.coe.uga.edu /emt668/EMAT6680.F99/Wise/essay9/essay9.htm (598 words)

	Divisibility rules for 4, 6, and 9 - Lesson plan from HomeschoolMath.net
		Numbers that are divisible by 2 end in __, __, __, __, or __.
		Division rule for 9 is similar to the division rule for 3.
		Use the divisibility rules and check if the number is divisible by 2, 3, 5, or 9.
	www.homeschoolmath.net /teaching/md/division_rules.php (597 words)

	Arithmetic, Numeration, Number Theory - Numericana
		Divisibility by 7, 13, and 91 (or by B
		Recall that a number is divisible by 3 or 9 iff (if and only if) the sum of its digits is. It is divisible by 11 iff the difference between the sum of its odd digits (units, hundreds, etc.) and the sum of its even digits (tens, thousands, etc.) is so divisible.
		Ruling out the zero function from multiplicative functions ensures that a unique multiplicative function is specified by values attributed to the prime powers, as stated next.
	home.att.net /~numericana/answer/numbers.htm (7644 words)

	Number Properties Section Print
		an integer that is divisible by 2 (0, 2, 4, 6, 8, 10).
		an integer not divisible by 2 (3, 5, 7, 9).
		Higher roots follow the same rule, and if a question asks for a fifth root of a number it means that a number raised to the fifth power will give us the original number.
	www.800score.com /content/arithmetic_print.htm (5263 words)

	Divisibility Rules
		I am a multiple of 5 that is less than 100 and is divisible by both 4 and 6.
		I am a 3-digit number between 200 and 300 that is divisible by 4 and 6.
		I am an odd number between 120 and 130 that is not divisible by 5 or 9.
	leader.education.louisville.edu /edtl/thompson/edem629/sum01/divisibilitywkst.htm (243 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)

	E-Database of Math, June, 1997 (Site not responding. Last check: 2007-10-26)
		The divisibility rule for three is that you add the digits of a number together, and if the sum is divisible by three, the original number is divisible by three.
		The proven divisibility rule for 3 stated that if three doesn't go evenly into the digit divided from, the original number (in this case 1,234) is not divisible by 3.
		Using the divisor 6 with the divisibility rule for 3, I found that it worked for 3 of the dividends I used, but not for the other 1.
	www.youth.net /nsrc/math/math005.html (3208 words)

	[No title]
		Apply a divisibility rule to predict whether a number is divisible by 2, 5, 10, 3 or 6. ActivitiesProcedures:First I will have the students get out their math materials and I will hand back their homework.
		I will tell them that the rule for figuring out if a number is divisible by 5 is whether the last digit has a 5 or a 0.
		I will demonstrate with an astronomically high number that is divisible by 5.I will have the students turn to page 202 in their math books and copy the purple table with the divisibility rules into their journal.
	home.twcny.rr.com /lugh/portfolio/fd.doc (1128 words)

	RichlandOne Interactive - Grade 7 Units/Lesson Plans
		After all of the rules have been discussed the teacher should give the students a number and then ask the students to use the rules to decide if it is divisible by 2?
		Students may wish to add some of the other rules as well, but the ones listed are a requirement.
		Label with P or C. You may use your divisibility rules.
	www.richlandone.org /resources/teacher_resources/connections/grade7/amiprime.htm (843 words)

	Math Trek: Testing for Divisibility, Science News Online, Aug. 17, 2002 (Site not responding. Last check: 2007-10-26)
		Because 15 is not divisible by 7, neither is 24598176.
		In the case of 7, the rule is sufficiently complicated that it takes nearly as much effort to check for divisibility as it would take to perform the division operation itself.
		Because 36 is not divisible by 19; the original number is not divisible by 19.
	sciencenews.org /articles/20020817/mathtrek.asp (1092 words)

	Number and Operations Session 5, Part B: Divisibility Tests
		Because 11 is one more than 10, the divisibility test for 11 is related to the test for 9.
		There are divisibility tests for 7 as well, but the calculations involved take longer than dividing by 7!
		Devise a general rule for a divisibility test for 16.
	www.learner.org /channel/courses/learningmath/number/session5/part_b/eleven.html (377 words)

	Divisibility by Seven
		There are also simple rules to determine whether a number is divisible by 3, 4, 5, 6, 8, 9, or 10.
		The known rules for testing for divisibility by 7 are amazingly cumbersome.
		For larger numbers, the rule is sufficiently complicated that it takes nearly as much effort to check for divisibility as it would be to perform the division operation itself.
	www.maa.org /mathland/mathtrek_05_23_05.html (693 words)

	Math Forum: Exploring Pascal's Triangle
		When they use Pascal's triangle to practice this rule, students are less likely to reach for their calculators to check for divisibility.
		The divisibility rule for three can be used to determine which numbers are one less than a multiple of three.
		The rule for divisibility for three can be used to determine which numbers are two less than a multiple of three.
	www.mathforum.org /workshops/usi/pascal/mid.color_pascal.html (590 words)

	Online Tutorials on Functions and Algebra
		Rules and Properties such as commutativity, associativity and distributivity of algebra with examples.
		Presentation of the rule for a 3 by 3 systems of equations.
		An example on using cramer's rule is presented.
	www.analyzemath.com /PrecalculusTutorials.html (654 words)

	Math Forum Discussions - Re: Divisibility rule for 7
		enough that you can tell without any help that it is divisible by 7.
		not divisible by either 2 or 5, but there are easier tests for 3, 9,
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	www.mathforum.com /kb/thread.jspa?forumID=13&threadID=1414053&messageID=4915683 (274 words)

	Divisibility by 7 and 11
		Your rule fro divisibility by 7 is correct.
		7 = 28 so 28 is divisible by 7, and hence 406 is divisible by 7, which insures 4102 is divisible by 7.
		which is not divisible by 11 so 678234 is not divisible by 11.
	mathcentral.uregina.ca /QQ/database/QQ.09.04/tammy1.html (312 words)

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