In competitive exams some time this type of questions come  if 61208 is divisible by 7 or is 113672 is divisible by 13.
Vedic maths divisibility test is an easy way know the divibility.
Given below are the divisibility test numbers in table form.
Divisible by  Condition 

2  Numbers ending with 0, 2,4,6,8 
3  Add up the digits. If the sum is divisible by 3 then number is divisible by 3 
4  If the number formed by the 2 digits is divisible by 4, then the whole number is diivisible by 4 
5  If the last digt is either 5 or 0. 
6  Check the divisibility test of 2 and 3. If divisible by 2 and 3 then it is divisible by 6. 
7  Double the last digit and subtract it from the remaining number. If what is left is divisible by 7, then the original number is also divisible. 
8  If the last three digits are divisible by 8, then the whole number is divisible by 8 
9  Add the digits if the sum is divisible by 9 then the whole number is divisible by 9. (this holds true for any poer of three. 
10  If the number ends in zero 
11  If the difference between

12  Check the divisibility by 3 and 4 
13  Delete the last digit from the given number, Then subtract 9 times the deleted digit from the remaining number. If what is left is divisible by 13, then so is the original number. 
In the same way we can continue the table.. for divisibility by 14, check fo divisibility by 2 and 7. For divisibility by 15, check for divisibility by 3 and 5 and so on.
Examples:
Is 25467895 is divisible by 5
Answer is yes because it has 5 last digit.
Example:
Is 2665 is divisible by 13?
Delete Last digits 5, sbtract 9X5=45 from 266 balance is 221. it is divisible by 13 so that whole number is divisible by 13.
Example:
If the number 4107501 is divisible by 9.
Answer. Add numbers 4+1+0+7+5+0+1=18, it is divisible by 9. So the number is divisible by 9.
Example:
If the number 12690864 is divisible by 8?
Answer: if last three numbers are divisible by 8 then whole number is divisible by 8. 864 is divisible by 8. Answer is yes.
"Vandana Sachar, M.A. Eco, teaching Vedic Maths for the last 15 years"
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