Problems based on Divisibility

Divisibility Rules for Common Numbers

1. Divisibility by 2
   A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).
2. Divisibility by 3
   A number is divisible by 3 if the sum of its digits is divisible by 3.
3. Divisibility by 4
   A number is divisible by 4 if the last two digits form a number divisible by 4.
4. Divisibility by 5
   A number is divisible by 5 if its last digit is 0 or 5.
5. Divisibility by 6
   A number is divisible by 6 if it is divisible by both 2 and 3.
6. Divisibility by 7
   To check divisibility by 7: Double the last digit, subtract it from the remaining number, and check if the result is divisible by 7. Repeat if necessary.
7. Divisibility by 8
   A number is divisible by 8 if the last three digits form a number divisible by 8.
8. Divisibility by 9
   A number is divisible by 9 if the sum of its digits is divisible by 9.
9. Divisibility by 10
   A number is divisible by 10 if its last digit is 0.
10. Divisibility by 11
    A number is divisible by 11 if the difference between the sum of its digits in odd and even positions is divisible by 11 or equals 0.
11. Divisibility by 12
    A number is divisible by 12 if it is divisible by both 3 and 4.
12. Divisibility by 13
    Multiply the last digit by 9, subtract it from the remaining number, and check if the result is divisible by 13.

Tips for Competitive RRB Exams

• Memorize shortcuts: Rules for numbers like 7, 11, and 13 may seem tricky but practicing a few examples makes them easier.
• Combine rules: For numbers like 6, 12, and 15, check the divisibility of their prime factors (e.g., 6 = 2 × 3).
• Practice mental math: Being quick at adding, subtracting, and multiplying digits helps in applying these rules efficiently.