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This is the list of all math-related draft pages in Draft as well as some in user pages (excluding redirects).

Usage

1. Divisibility by 12: The number should be divisible by both 3 3 3 and 4 4 4. Divisibility by 13: The sum of four times the units digits with the number formed by the rest of the digits must be divisible by 13 13 1 3 (this process can be repeated for many times until we arrive at a sufficiently small number).
2. Divisibility and Greatest Common Divisors. To install LaTeX for a Mac use MacTeX and as a front end use Texmaker.
3. Chapter 1 Divisibility Rules study guide by MrDunkel includes 8 questions covering vocabulary, terms and more. Quizlet flashcards, activities and games help you improve your grades.

• Add pages in the draftspace that are within the scope of WikiProject Mathematics (excluding redirects). Remove them as they get moved, redirected or deleted. If necessary, note the removal in the talkpage.
• Similarly add/remove a draft page in your user page, if you wish, to let the others know about it (to avoid duplicated efforts).

See also

• the subpages of User:Math-drafts, which is a user page used as an alternative to the draftspace.
• Category:Drafts about mathematics.

Concepts[edit]

Geometry[edit]

Divisibility Rule for 9. Same rule for 3. You add up all the numbers and see if the answer is divisible by 9. Divisibility Rule for 10. The last digit should be 0. Divisibility rules or Divisibility tests have been mentioned to make the division procedure easier and quicker. If students learn the division rules in Maths or the divisibility tests for 1 to 20, they can solve the problems in a better way. For example, divisibility rules for 13 help us to know which numbers are completely divided by 13.

• Draft:Faithfully flat descent - partially published to faithfully flat descent
• User:Math-drafts/Hamiltonian group action - has a broader scope than moment map
• Draft:Residual intersection - the page has been published in mainspace except one incomplete section
• Draft:Pentacontahenagon - not sure if it is notable or not.

Algebra, algebraic topology and category theory[edit]

• Draft:Division by infinity - needs further cleanup, but could be a good counterpart to division by zero
• Draft:Eigencircle of a 2x2 matrix - it probably makes sense to have eigencircle first though.
• Draft:Frobenius formula - work out the derivation that will be put back to Frobenius formula
• Draft:Correspondence (mathematics) - should be merged with binary relation

Mathematical analysis[edit]

• Draft:Lie's formula keep at Wikipedia:Miscellany_for_deletion/Draft:Lie's_formula_(2nd_nomination) in Feb 2018
• Draft:Bose integral - need a lot more work but the topic seems legit
• Draft:Leimkuhler-Matthews method - likely notable

1.3 Divisibility Rulesmr. Mac's Page Shortcut

Differential equations and dynamical system[edit]

• Draft:Separable ordinary differential equation - likely covered already in mainspace

Representation theory (including invariant theory)[edit]

Probability and statistics[edit]

• Draft:Vecchia approximation - a page moved from mainspace for incubation

1.3 Divisibility Rulesmr. Mac's Page Printable

Number theory[edit]

• Draft:Power of 6 - barely a stub
• Draft:Gaussian symbol - probably should be part of some existing article

Mathematical physics[edit]

• Draft:Axiomatic thermodynamics - (the question 'is thermodynamics axiomatic' seems controversial but perhaps that deserves the discussion.)
• Draft:Heaviside-Feynman formula - would be ready to go if a couple secondary sources were provided

Combinatorics and graph theory[edit]

• Draft:Counting lemma - seems notable? it's related to Graph removal lemma (but perhaps a separate article is warranted).

Logic and set theory[edit]

• Draft:Mathematical correspondence - should probably be merged With binary relation

Others[edit]

• Draft:Universal approximation theorem - need to be merged with Universal approximation theorem

Mathematicians[edit]

Put them in the alphabetical order (last name). Also, for the sake of efficiency, add only those who seem to have some potential of satisfying the notability requirement.

• Draft:Tomoyuki Arakawa - likely notable as an invited speaker at ICM
• Draft:Elena Mantovan - unclear notability
• Draft:Oscar Garcia Prada - not sufficiently notable?
• Draft:Kasia Rejzner - notability is in dispute
• Draft:Wilhelm Schlag - an invited speaker at ICM

Miscellaneous[edit]

Uncategorised[edit]

• User:TakuyaMurata/sandbox - please do not edit it but if you find some materials useful, you’re welcome to use them in the main or draft space.

Divisibility Rules are useful when you want to find out if the given big number is exactly divisible or not without actually dividing.
This saves a lot of time which is the need of the hour in any competitive exam. This shortcut is especially handy when you are solving Problems on Ages. We shall find out if a number is divisible by 2,3,4,5,6,7,8,9,10,11,13 using various divisibility rules.

Divisibility Rules | Number divisible by 2

To check if the given number is exactly divisible by 2 follow the below steps
Step 1: Check if the units digit of the given number is even.
Step 2: If the units digit is even, the given number is exactly divisible by 2.
If not, the given number is not exactly divisible by 2.

Example 1:Is 584 exactly divisible by 2.
Step 1: We see that the units digit (4)is an even number.
Thus, we can say that 584 is exactly divisible by 2.

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Example 2: Is 627 exactly divisible by 2.
Step 1: We see that the units digit (7)is an odd number.
Therefore, we can conclude that 627 is not exactly divisible by 2.

Divisibility Rules | Number divisible by 3

To check if the given number is exactly divisible by 3 follow the below steps
Step 1: Add all the digits in the given number until you arrive at a single number.
Step 2: If the single number arrived is 3, 6, 9, then, the given number is exactly divisible by 3. If not the given number is not exactly divisible by 3.

Example 1: Is 95 exactly divisible by 3.
Adding we get, 9 + 5 = 14
Further adding we get,1 + 4=5
we know that 5 is not exactly divisible by 3.
Thus, we can conclude that 95 is not exactly divisible by 3.

Example 2: Is 63 exactly divisible by 3
Adding we get, 6 + 3=9
We know that 9 is exactly divisible by 3.
Therefore, 63 is exactly divisible by 3.

Divisibility Rules | Number divisible by 4

To check if the given number is exactly divisible by 4 follow the below steps
Step 1: Check if the last two digits of the given number are divisible by 4.
Step 2: If divisible then, the entire number is divisible by 4.
If not, then the entire number is not divisible by 4.

Example 1: Is 624 divisible by 4?
Step 1: Dividing last 2 digits(24) by 4.
We know that 24 is exactly divisible by 4.
So, we can conclude that the given number 624 is also exactly divisible by 4.

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Example 2: Is 514 divisible by 4?
Step 1: Dividing last 2 digits(14) by 4.
We know that 14 is not exactly divisible by 4.
So, we can conclude that the given number 514 is also not exactly divisible by 4.

Divisibility Rules | Number divisible by 5

To check if the given number is exactly divisible by 5 follow the below steps
Step 1: If the given number ends in 0 or 5 it is exactly divisible by 5.
If not then, the given number is not exactly divisible by 5.

Example 1: Is 1015 divisible by 5?
Step 1: We see that the given number ends in 5
Thus, we can say that 1015 is exactly divisible by 5.

Example 2: Is 5551 divisible by 5?
Step 1: We see that the given number ends in 1
So, we can conclude that 5551 is not exactly divisible by 5.

Divisibility Rules | Number divisible by 6

To check if the given number is exactly divisible by 6 follow the below steps
Step 1: Check if the given number is Even number.
Step 2: Find the sum of all the digits of the number until you arrive at a single number.
Step 3: If the single number arrived is 3, 6, 9, then, the given number is exactly divisible by 6. If not the given number is not exactly divisible by 6.

Example 1: Is 846 divisible by 6?
Step1: We see that the given number is an even number.
Step 2: Add the digits we get, 8 + 4 + 6=18
Again adding we get, 1 + 8= 9
Therefore, the given number 846 is exactly divisible by 6.

Example 2: Is 825 divisible by 6?
Step 1: We see that the given number is an odd number.
Step 2: Add the digits we get,8 + 2 + 5=15
Further adding we get, 1 + 5 =6
Even though the sum of the digits is 6, the given number is not exactly divisible by 6 as the given number is odd number.

Divisibility Rules | Number divisible by 7

To check if the given number is exactly divisible by 7 follow the below steps
Step 1: Multiply the last digit of the given number by 2.
Step 2: Subtract the result obtained in step 1 from the remaining digits of the given number.
Step 3: If the result obtained in Step 2 is either 0 or a number divisible by 7 then, the given number is exactly divisible by 7. If not then, the given number is not exactly divisible by 7.

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Example 1: Is 259 divisible by 7?
Step 1: Multiplying the last digit by 2 we get, 9 X 2=18
Step 2: Subtracting the result we get, 25 – 18= 7
Step 3: We know that 7 is exactly divisible by 7
So we can conclude that 259 is exactly divisible by 7.

Example 2: Is 123 divisible by 7?
Step 1: Multiplying the last digit by 2 we get, 3 X 2=6
Step 2: Subtracting the result we get, 12 – 6= 6
Step 3: We know that 6 is not exactly divisible by 7
Thus, we can say that 123 is not exactly divisible by 7.

Divisibility Rules | Number divisible by 8

To check if the given number is exactly divisible by 8 follow the below steps
Step 1: Check if the given number is Even number.
Step 2: Check if the last 3 digits of the given number is divisible by 8.
Step 3: If divisible then, it is exactly divisible by 8. If not then, it is not exactly divisible by 8.

Example 1: Is 2016 divisible by 8?
Step 1: We see that the given number is an even number.
Step 2: The last 3 digit that is 016 is exactly divisible by 8.
Step 3: Thus, we can conclude that the given number 2016 is exactly divisible by 8.

Example 2: Is 2124 divisible by 8?
Step 1: We see that the given number is an even number.
Step 2: The last 3 digits that is 124 is not exactly divisible by 8.
Step 3: So, we can say that the given number 2124 is not exactly divisible by 8.

Divisibility Rules | Number divisible by 9

To check if the given number is exactly divisible by 9 follow the below steps
Step 1: Add all the digits of the number.
Step 2: If the number obtained is 9 or a multiple of 9, then the given number is exactly divisible by 9.
If not then, the given number is not exactly divisible by 9.

Example 1: Is 4513 divisible by 9?
Step 1: Adding the digits in the given number we get, 4+5+1+3=13
Step 2: We know that 13 is not divisible by 9.
Step 3: Thus, we can say that the given number is not exactly divisible by 9.

Example 2: Is 3555 divisible by 9?
Step 1: Adding the digits in the given number we get, 3+5+5+5=18
Step 2: We know that 18 is exactly divisible by 9.
Step 3: Thus, we can say that the given number is exactly divisible by 9.

Divisibility Rules | Number divisible by 10

To check if the given number is exactly divisible by 10 follow the below steps
Step 1: If the last digit of the given number is 0 then it is exactly divisible by 10.
Step 2: If not then, the given number is not exactly divisible by 10.

Example 1: Is 5510 divisible by 10?
Step 1: Here, we see that the last digit of the given number is 0.
Thus, we can say that the given number is divisible by 10.

Example 2: Is 6201 divisible by 10?
Step 1: Here, we see that the last digit of the given number is not 0.
Thus, we can say that the given number is not exactly divisible by 10.

Divisibility Rules | Number divisible by 11

To check if the given number is exactly divisible by 11 follow the below steps
Step 1: Find alternative digits in the given number and make 2 separate groups.
Step 2: Find the sum of the digits within each group.
Step 3: Find the difference between the 2 sums.
Step 4: If the difference in the sums is equal to 0 or 11 or multiple of 11, then the given number is exactly divisible by 11.
If not then, the given number is not exactly divisible by 11.

Example 1: Is 5962 divisible by 11?
Step 1: Finding alternative digits and grouping
we get, 5 and 6 -group A and 9 and 2- group B
Step 2: Finding sum of the digits
we get, Group A- 5+6=11 and Group B- 9+2=11
Step 3: Finding the difference between group A and group B
we get, 11-11=0
Step 4: We see that the difference is 0. Therefore, we can say that the given number 5962 is exactly divisible by 11

Example 2: Is 3431 divisible by 11?
Step 1: Finding alternative digits and grouping
we get, 3 and 3 -group A and 4 and 1- group B
Step 2: Finding sum of the digits
we get, Group A- 3+3=6 and Group B- 4+1=5
Step 3: Finding difference of group A and group B
we get, 6-5=1
Step 4: We see that the difference is not 0 or multiple of 11. Best free antivirus software and apps 2018 for mac osx. Thus, we can say that the given number 3431 is not exactly divisible by 11

Divisibility Rules | Number divisible by 13

To check if the given number is exactly divisible by 13 follow the below steps Step 1: Find alternative groups of 3 digits from the given number starting from the right. One alternative group to be group A and another alternative group to be Group B.
Step 2: Add the alternative Group A and Group B to arrive at two sums.
Step 3: Find out the difference between the 2 sums.
Step 4: If the difference is equal to 0 or a multiple of 13 then, the given number is exactly divisible by 13.
If not the given number is not exactly divisible by 13.

Example 1: Is 2,456,121,241,514 divisible by 13?
Step 1: Finding alternative groups
We get, Group A- 514,121,2
And Group B- 241,456
Step 2: Adding the alternative Groups
We get, Group A =514+121+2=637
Group B= 241+456=697
Step 3: Finding the difference between the 2 sums.
We get, Group A- Group B- 637-697=60
Step 4: We see that the difference(60) is neither equal to 0 nor a multiple of 13. Thus ,the given number is not exactly divisible by 13.

Example 2: Is 32,903 divisible by 13?
Step 1: Finding alternative groups
We get, Group A-903
And Group B-32
Step 2: Adding alternative Groups.This step can be skipped as there is only 1 number in the group.
We get, Group A=903 and Group B=32
Step 3: Finding the difference between the 2 sums.
We get, Group A- Group B- 903-32=871
Step 4: We see that the difference(871) is a multiple of 13. Thus, the given number is exactly divisible by 13.