Divisibility Rules From 7 to 11
To find out if a number is divisible by 7, take the last digit, double it, and subtract it from the rest of the number. If you get an answer divisible by 7 (including zero), then the original number is divisible by 7. If you don’t know the new number’s divisibility, you can apply the rule again.
In the Above Example to Double the Last Digit of the Given Number i.e. 8 and Subtract it from the rest. i.e. 155-8 = 147 which is divisible by 7.
If the Last 3 digits of the Number are 000 or Divisible by 8 then the whole number will Divisible by 8.
Ex: 158000, 325676
In the above Example we find one number has last 3 digits of zeros (000) and in another number, the Last 3 digits are divisible by 8. Then Both of the above Numbers will Divisible by 8.
The rule for 9 is as Same as rule for 3. Sum of the Digits of Given Number is Divisible by 9.
In the Above Example, the sum of all the digits is 2+1+6+9+9 = 27, which is divisible by 9. So, the Whole number will be divisible by 9.
If a number is Divisible by 10 when the units Digit of the Number is ‘0’.
Ex: 15250, 28600
In the Above Example the last digit of the Given Number is 0 then the whole number is divisible by 10.
The difference between the Alternative digits of the Given Number is ‘0’ or Multiple of 11. Then the Whole number will be divisible by 11. (Units Digit First)
Ex 1: 674531
In the Above Example, the difference between the Alternate digits is
1+5+7 = 13
3+4+6 = 13
I.e. 13 – 13 = 0
Then the whole number is divisible by 11.
Ex 2: 399949
Here the Difference Between the Alternative Digits is 9+9+9 = 27
9+9+9 = 27
4+9+3 = 16
i.e. 27 – 16 = 11 (Which is the Multiple of 11)
So, the Number Must be Divisible by 11.
By Using these Divisibility Rules we can find divisibility of any Given Number.