Algebra Den

Divisibility Principle of 11

Definition :-
The Divisibility Principle of 11 involves following steps :-
Step.1) From the right, add all the digits of the given number which are at odd places.
Step.2) From the right, add all the digits of the given number which are at even places.
Step.3) Find the difference of step 1 & step 2.
Step.4) If the difference (in step 3) is either 0 or divisible by 11, then the given number is also divisible by 11
In other words, if the difference, of the odd place digit and even place digit from right of a given number, is either 0 or divisible by 11, then the given number is also divisible by 11.

Example 1 = Is 286 divisible by 6 ?
Answer = Step 1. From right, find digits at odd places in the given number, and these are 2 and 6,
On additon of digits in odd places, we get,
2 + 6 = 8
Step 2. From right, find digits at even places in the given number, and which is 8,
Step 3. Find the difference of sum of digits in odd and even places and we get,
8 - 8 = 0
Since the difference is 0 (Zero), so we can say the given number 286 is divisible by 11.

Example 2 = Is 984 divisible by 6 ?
Answer = Step 1. From right, find digits at odd places in the given number, and these are 4 and 9,
On additon of digits in odd places, we get,
4 + 9 = 13
Step 2. From right, find digits at even places in the given num, and which is 8,
Step 3. Find the difference of sum of digits in odd and even places and we get
13 - 8 = 5
Since the difference is 5, which is not divisible by 11, so we can say the given number 984 is also not divisible by 11.

Example 3 = Is 1078 divisible by 6 ?
Answer = Step 1. From right, find digits at odd places in the given number, and these are 8 and 0,
On additon of digits in odd places, we get,
8 + 0 = 8
Step 2. From right, find digits at even places in the given number, and these are 7 and 1,
On additon of digits in even places, we get,
7 + 1 = 8,
Step 3. Find the difference of sum of digits in odd and even places and we get
8 - 8 = 0
Since the difference is 0 (Zero), so we can say the given number 1078 is divisible by 11.

Example 4 = Is 7490 divisible by 6 ?
Answer = Step 1. From right, find digits at odd places in the given number, and these are 0 and 4,
On additon of digits in odd places, we get,
0 + 4 = 4
Step 2. From right, find digits at even places in the given number, and these are 9 and 7,
On additon of digits in even places, we get,
9 + 7 = 16,
Step 3. Find the difference of sum of digits in odd and even places and we get
16 - 4 = 12
Since the difference is 12, which is not divisible by 11, so we can say the given number 7490 is also not divisible by 11.

Example 5 = Is 86515 divisible by 6 ?
Answer = Step 1. From right, find digits at odd places in the given number, and these are 5, 5 and 8,
On additon of digits in odd places, we get,
5 + 5 + 8 = 18
Step 2. From right, find digits at even places in the given number, and these are 1 and 6,
On additon of digits in even places, we get,
1 + 6 = 7,
Step 3. Find the difference of sum of digits in odd and even places and we get
18 - 7 = 11
Since the difference is 11, which is divisible by 11, so we can say the given number 7490 is divisible by 11.

Example 6 = Is 62809 divisible by 6 ?
Answer = Step 1. From right, find digits at odd places in the given number, and these are 9, 8 and 6,
On additon of digits in odd places, we get,
9 + 8 + 6 = 23
Step 2. from right, find digits at even places in the given number, and these are 0 and 2,
On additon of digits in even places, we get,
0 + 2 = 2,
Step 3. Find the difference of sum of digits in odd and even places and we get
23 - 2 = 21
Since the difference is 21, which is not divisible by 11, so we can say the given number 7490 is also not divisible by 11.