DIVISIBILITY RULESRules, 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.

….CONTENTS….1. Divisibility By 2 9. Divisibility By 10

2. Divisibility By 3 10. Divisibility By 113. Divisibility By 4 11. Divisibility By 124. Divisibility By 55. Divisibility By 66. Divisibility By 77. Divisibility By 88. Divisibility By 9

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.

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

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 : 457994 + 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

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.

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

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.

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.

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.

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 means 9 divide evenly 92745.

And if you’ll divide evenly with 3 after then it also divide 27.

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

means the unit place doesn’t contain 0, so these can’t divide by

10.

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 numbers2. 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 because1. (6+1+5+5) – (6+3+8)2. 17-17 = 0,.3. Example : 7890 is not divisible by 11 because4. (7+9) – (8+0)5. 16-8 = 8, we have 8 as remainder

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