Number System : Divisibility by 7
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Take the last digit off the number.
Double it and subtract the doubled number from the remaining number.
If the result is evenly divisible by 7 (e.g. 14, 7, 0, -7, etc.), then the number is divisible by seven. You may have to repeat the steps several times.
Example :
Lets take an example 4293(say).
step 1: Double the last digit -> 3×2=6
step 2: Subtract it from the remaining number -> 429-6=423
step 3: repeat the above steps to check 423 is divisible by 7 or not -> 3×2=6 ->42-6=36 which is clearly not divisible by 7.
So the number 4293 is not divisible by 7.
Since to check divisibility by 7 is a bit cumbersome process. We can check it by simply dividing the number by 7.
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One more method is there, especially for larger numbers:
The number will be divided by 7, if and only if the difference of the number of its thousands and the reminder of its division by 1000 is divisible by 7.
Example: 770546 is divisible by 7 or not.
Solution: 770-546 = 224
224/7 = 32
So, 770546 is divisible by 7.
Note: Same rule applies for 11 and 13 also.