Rules of Divisibility – Number Systems | General Aptitude for GATE, PSU, ESE, AE/JE

The Rules of Divisibility are important shortcuts in Number Systems that help you quickly determine whether a number is divisible by another number without performing full division. These rules are extremely useful for exams like GATE, PSU, ESE, AE/JE, SSC, and Banking.

What is Divisibility?

A number is said to be divisible by another number if it leaves no remainder when divided.

Example: 24 is divisible by 6 because 24 ÷ 6 = 4 (no remainder)

Important Divisibility Rules

Number	Divisibility Rule	Example
2	Last digit is even (0, 2, 4, 6, 8)	246 → divisible
3	Sum of digits divisible by 3	123 → 1+2+3=6 → divisible
4	Last 2 digits divisible by 4	316 → 16 ÷ 4 = 4
5	Last digit is 0 or 5	145 → divisible
6	Divisible by both 2 and 3	132 → divisible
7	Double last digit and subtract from remaining number (repeat process)	203 → 20 - (2×3) = 14 → divisible
8	Last 3 digits divisible by 8	1000 → 000 ÷ 8 = 0
9	Sum of digits divisible by 9	729 → 7+2+9=18
10	Last digit is 0	450 → divisible
11	Difference of sum of alternate digits is 0 or multiple of 11	121 → (1+1)-2 = 0

Understanding with Examples

Example 1: Is 456 divisible by 3?

Sum = 4 + 5 + 6 = 15 → divisible by 3
So, Yes, it is divisible by 3.

Example 2: Is 728 divisible by 4?

Last 2 digits = 28 → divisible by 4
So, Yes

Example 3: Is 1331 divisible by 11?

(1 + 3) - (3 + 1) = 4 - 4 = 0
So, Yes, divisible by 11

Shortcut Tips for Exams

Always check last digit rules first (2, 5, 10)
Use digit sum for 3 and 9
Remember: 6 = 2 + 3 condition
Practice rule of 7 and 11 carefully (frequently asked)

Common Mistakes to Avoid

Forgetting to check both conditions for 6
Wrong addition of digits for 3 and 9
Confusing rules of 4 and 8

Practice Questions

Is 864 divisible by 8?
Is 999 divisible by 9?
Is 121 divisible by 11?
Is 245 divisible by 5?

Conclusion

Divisibility rules are powerful tools that help you solve problems quickly and efficiently in competitive exams. Mastering these rules can save valuable time and improve your accuracy in General Aptitude sections of GATE, PSU, ESE, and other exams.

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