Divisibility Rules of the rules of the number 2,3,4,5,6,7,8,9,10,11 given below
Basically, Divisibility rules are classified into two groups
Root numbers and Non root numbers
Root numbers know simply as prime number like 2,3,5,7,11
Other than the roots words are called Non root numbers or non prime number
I will clearly explain this root words after the learning the divisibility rules of the Root numbers
Divisibility Rule of ''2'':
When a number is divisible by 2 then the last digit of the number must be divisible by 2
For example : 64
In the above number last digit is "4" which is a multiple of 2 .Clearly, we can say that the above number 64 is divisible by 2
Normal checking: 64/2=32
The above statement is verified
Similarly, for different powers of " 2 " mean non-roots words like 2^2=4, 2^3=8,-----
Divisibility rule for 2^1=2, we had checked the last digit of the number is divisible by 2
for 2^2=4 we need to check the last 2 digits of the number must be divisible by 4 then the whole number is divisible by 4
For example, Is 2345677808 divisible by 4
On sight, we can say that last two digits " 08" divisible by 4
then the whole number is divisible by " 4 "
Similarly, depending on the power of the 2 we need to take the last digits to check whether the number is divisible by that number r not
If the divisibility of
2^2=4, it is the second power of 2 so we need to check whether last two digits of the number are divisible 4 or not
2^3=8,it is the third power of 2 so we need to check whether last three digits of the number are divisible by 8 or not
2^4=16,it is a fourth power of 2 so we need to check whether last four digits of the number are divisible by 16 or not
Similarly, for all power of the two, we need to check depending on the power and the last digits of the number
For Example,
Is it 6348394863847634986734837568 divisible by 8
as we know that 8 is the third power of 2
We check that last three digits of the number 568 are divisible by 8
568/8=71, so that whole number is divisible by 8
Divisibility Rule of 3:
When a number is divisible by " 3 " then the sum of the all the digits must be divisible by 3
For Example(1), 93
In the above number, there are two digits 9and 3
the sum of the two digits 3+9=12 and check whether sum is divisible 3 r not Clearly, the sum 12 is divisible by 3 then 93 is divisible by 3
(2) 123456789
In the above number, there are 9 digits
the sum of all the digits 1+2+3+4+5+6+7+8+9=45
45 is divisible by 3 then the whole number is divisible by 3
For the powers of " 3 "
3^2=9, if the sum of the digits divisible by 9 then the whole number is divisible by 9
3^3=27, if the sum of the digits divisible by 27 then the whole number is divisible by 27
For Example: 585
sum of the 585 is 5+8+5=18
We know 18 is divisible by 9 then the number 585 is divisible by 9
Divisibility Rule of "5":
Of all the divisibility rules, Divisibility rule of 5 is very easy we can easily said at fraction of seconds
If the last digit of the number is either 5 or 0 then we can easily said that the whole number is divisible by 5
For Example:
Is the number 4356534354565345 divisible by 5?
Our answer is YES
On seeing last digit of the number i.e, 5 We simply said that the number is divisible by 5
Divisibility Rule of " 7 ":
If a number is divisible by " 7 ", The last digit of the number is doubled and subtracted from the remaining number if the obtaining number is divisible by 7 then the whole number is divisible by " 7 "
For Example: 3024
the last digit of the number is, double the number
i.e,4*2=8
Subtract that number from the remaining number i.e, 302 -8=294
At this we use to check directly by 7 or we can do another iteration to get direct multiple of the 7
Again from 294, the last digit is doubled and subtracted from the remaining number
29-4*2=29-8=21
on sight, we can say that 21 is divisible of 7 then the whole number is divisible by "7"
Another Example:
Is it 398874 is divisible of 7?
Iteration 1: double the last digit and subtract form the number
39887-4*2=39887-8=39879
Iteration 2: again do the same thing double and subtract
3987-9*2=3987-18=3969
Iteration 3: Repeat
396-9*2=396-18=378
Iteration 4:Repeat
37-8*2=37-16=21
on sight that 21 is divisible by 7
therefore the whole number is divisible by 7
Divisibility Rule of "11":
SPECIAL RULE:
The special divisibility rule of 11 is successive subtracting the digit values from previous digit place it start from the last digit
For Example:
(1) 1342
last digit from the above number is 2 subtract from the previous digit value =134-2=132
Repeat once last digit of 132 is 2 subtract from 3
=13-2=11
From the above answer 11 it is divisible by 11
Therefore, the whole number is divisible by 11
First Rule:
To verify the divisibility rule of 11, the subtracted value from the sum of even digits place value to sum of odd digits place value is divisible by 11 then the whole number is divisible by 11
For Example:
(1)1342
sum of the even place digits value = 3+2=5
sum of the odd place digits value = 1+4=5
subtract both=5-5=0
If the any divisibility we get " 0 " as your answer then it obey's your divisibility rule
(2) 29435417
sum of the odd place digits value = 2+4+5+1=12
sum of the even place digits value=9+3+4+7=23
subtract both=23-12=11
on the sight the result is divisible by 11
Then the given number is divisible by 11
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