This document discusses divisibility rules for numbers 0-12. It provides shortcuts to determine if a number is divisible by certain divisors without performing long division. For each rule, it explains the pattern to look for in the digits of the number. For example, a number is divisible by 2 if its last digit is even, by 5 if its last digit is 0 or 5, and by 11 if adding all even and odd digits separately and subtracting the results equals 0. The document aims to teach efficient ways to test divisibility through brief explanations and examples.

1. DIVISIBILITY RULES
Rules, Rules, Rules – no one likes to follow the rules, But
sometimes there are good rules, like the ones that allows you
to do less work ! Well these are the kind of rules that you will
find in this Power Point Presentation. There are many
shortcuts and tricks that allows you to test whether a number,
or dividend, is divisible by a given divisor. This Power Point
Presentation focuses on you the most – frequently studied
Divisibility rules which involve divisibility by 0, 1, 2, 3, 4, 5, 6,
7, 8, 9, 10, 11 and 12.

2. ….CONTENTS….
1. Divisibility By 2 9. Divisibility By 10
2. Divisibility By 3 10. Divisibility By 11
3. Divisibility By 4 11. Divisibility By 12
4. Divisibility By 5
5. Divisibility By 6
6. Divisibility By 7
7. Divisibility By 8
8. Divisibility By 9

3. DIVISIBILITY OF 0 AND 1
 Each and every number is
divisible by 0 except 0
itself because it is not
defined i.e. 0 / 0 = not
defined otherwise the
quotient is always zero.
 Each and every number is
divisible by 1 and the
quotient is always such the
number itself.

4. DIVISIBILITY RULE OF 2
 Any whole number which unit place is an even number i.e. 2,4,6,8,0 or a
multiple of two, is divisible by 2 .
 For Example : 456794852 and 2,98,76,543
 We can say if 2 divides these numbers with remainder zero by just
looking at the unit places of these numbers.
 Let’s start with the number 456794852 = The units place is ‘2’. This
means the number is an even and two will divide it with remainder
ZERO.
 So 456794852 is divisible by 2.
 2,98,76,543 = the unit place is not even, i.e. 3
 So 2,98,76,543 is not divisible by 2

5. DIVISIBILTY RULE OF 3
 A number is divisible by 3, if the sum of the operation is divisible by 3. What does
this means ? this means that we need to add up the digits in operation and see the
answer is evenly divided by 3 or 0 as a remainder.
 Example : 34911
 Add up the digits. 3 + 4 + 9 + 1 + 1 = 18.
 If 3 divides evenly the sum 18. Yes, 3x6 = 18.
 So 3 evenly divides 18. So, 3 is factor of 34911.
 Example : 45799
4 + 5+7 + 9 + 9 = 34
 3 does not divide evenly The operation 34
 Therefore, 3 does not divide evenly 45799. so 3 is not a factor of 45799

6. DIVISIBILTY RULE OF 4
 If the number made by the tenth and unit place of any number is
divisible by 4, then the entire number is divisible by 4.
 Example : 456791824 and 723810
 456791824 = Does 4 is evenly divide into 24 ? Yes. That means 4 will
also divide evenly into 456791824 and there will no remainder.
 723810 = Again we will look at tenth and unit place. Does 4 evenly
divide into 10 ? No, that means 4 will not divide evenly into 723810
and there will be a remainder.

7. DIVISIBILITY RULE OF 5…
 We can check it easily that the number that are
divisible by 5 its units place must be ‘0’ or ‘5’.
 Example : 34,780
 For this rule we check the unit place and it is zero
means it is divisible by 5.
 Example : 13,569
 Again, we will focus our attention ate the units place-
the last digit is 9, so this number is divisible by 5

8. DIVISIBILITY RULE OF 6
 The prime factors of 6 are 2 and 3. so for a number to be divisible by 6, it must also be
divisible by 2 and 3. therefore we need to check even and then check the sum of operation is
divisible by 3.
 Example : 23908
 Determine if the number is even, the unit place is 8 that means its an even, therefore it is
divisible by 2. Add the digits 2+3+9+0+8 = 22. 3 does not divide evenly 22. So this number is
not divisible by 3.
 Example ; 154608
 This number is even therefore it is divisible by 2. add the digits 1+5+4+6+0+8 = 24. 24 is
divisible by 3 because 3x8 = 24.
 Because the operation is divisible by 2 and 3, therefore it is divisible by 6.

9. DIVISIBILITY RULE OF 7
 A number is divisible by seven if the following are applying true:
1. Multiply the unit place by 2.
2. Subtract this value from the rest of the number.
3. Contine the method until unless you will find a divisibility by 7 that
you know very well.
 Example : 7203 is divisible by 7 because:
 3*2 = 6 = 714 which is divisible by 7
 Example ; 14443 is not divisible by 7 because :
 3*2 = 6 = 1444-6 = 1438
 8*2 = 16 = 143-16 = 127 which is not divisible by 7
 Note : this method takes a ot of practice and is sometimes easier to
work individually.

10. DIVISIBILITY RULE OF 8
 If the number made by the hundredth, tenth and unit place of any number
is divisible by 8, then the entire number is divisible by 8.
 Example : 456791824
 Does 8 divide evenly into 824? Yes. 8 goes into 824, 103 times without left
over. So this number is divisible by 8.
 Example : 923780
 Does 8 divide evenly into 780? No. 8 goes into 780, 97 times with a
remainder of 4.so this number is not divisible by 8.
 The rules for 2,4,8 should all looks similar because these numbers are
related. Think about the powers of 2:
21=2
22=4
24=8
 The exponent, or power of 2, used is also the number of digits that we have
to use when performing the text.

11. DIVISIBILITY RULE OF 9
 The prime factor of 9 is 3. So we can use a very similar rule
to determine if a number is divisible by 9. Basically, we see
the sum of the digits that is divisible by 9. If it is then the
actual number is also divisible by 9. This is done by the same
way that we done the rule of 3.
 Example : 871989
 Add up the digits 8+7+1+9+8+9 = 42. 9 is not evenly divide
into 42 because 9*4 = 36 and 9*5 = 45, so 9 does not divide
evenly 871989.
 Example ; 92745
 sum the operation 9+2+7+4+5 = 27. 9 goes into 27 three
times because 9*3 = 27. because 9 is divide evenly 27, That

12. DIVISIBILITY RULE OF 10
 We can check it easily that the number that are divisible by
10, its units place must be ‘0’ i.e. the last digit of the number
must be 0
 e.g. 1346790, 6781230, 111111199995550 all numbers are
ending with 0 implies these numbers are divisible by 10
 Example : 65442, 65342789, 9876543421 aren't ending with 0

13. DIVISIBILITY RULE OF 11..
 Divisibility rule of 11 is typical but interesting. A number is
divisible by 11 if it applies these instructions:
1. Find out all the even and odd numbers
2. Add the remaining digits together and Subtract odd to odd
and even to even. If its value is ‘0’ then the number is
divisible by 11. if it is not 0 then the remainder should be a
multiple of 11, then only it is divisible by 11.
 Example : 6613585 is divisible by 11 because
1. (6+1+5+5) – (6+3+8)
2. 17-17 = 0,.
3. Example : 7890 is not divisible by 11 because
4. (7+9) – (8+0)
5. 16-8 = 8, we have 8 as remainder

14. DIVISIBILITY RULE OF
12 The divisibility rules of 3 and 4 applies on a operation and the
remainder will be ‘0’ that means the operation is divisible by 12.
 Example : 648
 Add the digits 6+4+8 = 18. 18 evenly divide 3 because 3*6 = 18.That
means 648 is divisible by 3.
 Take the unit and tenth place and divide it with 4. 48 / 4 = 12, 0 as a
remainder. So it is divisible by12.
 Example : 524
 Ad all the digits 5+2+4 = 11, which is not divisible by 3 because 3*3 =
9 and 3*4 = 12. If one rule is not applying so no need to check the
another. It is not divisible by 12