divisibility rule for 11??
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Answer:
Divisibility Rules for 11
If the difference of the sum of alternative digits of a number is divisible by 11, then that number is divisible by 11 completely.
In order to check whether a number like 2143 is divisible by 11, below is the following procedure.
Group the alternative digits i.e. digits which are in odd places together and digits in even places together. Here 24 and 13 are two groups.
Take the sum of the digits of each group i.e. 2+4=6 and 1+3= 4
Now find the difference of the sums; 6-4=2
If the difference is divisible by 11, then the original number is also divisible by 11. Here 2 is the difference which is not divisible by 11.
Therefore, 2143 is not divisible by 11.
A few more conditions are there to test the divisibility of a number by 11. They are explained here with the help of examples:
If the number of digits of a number is even, then add the first digit and subtract the last digit from the rest of the number.
Example: 3784
Number of digits = 4
Now, 78 + 3 – 4 = 77 = 7 × 11
Thus, 3784 is divisible by 11.
If the number of digits of a number is odd, then subtract the first and the last digits from the rest of the number.
Example: 82907
Number of digits = 5
Now, 290 – 8 – 7 = 275 × 11
Thus, 82907 is divisible by 11.
Form the groups of two digits from the right end digit to the left end of the number and add the resultant groups. If the sum is a multiple of 11, then the number is divisible by 11.
Example: 3774 := 37 + 74 = 111 := 1 + 11 = 12
3774 is not divisible by 11.
253 := 2 + 53 = 55 = 5 × 11
253 is divisible by 11.