Divisibility rules help us quickly determine whether a number is completely divisible by another without performing full division. Mastering these rules is essential for competitive exams, saving time in problem-solving. Let's explore these rules with examples and shortcut techniques using Vedic mathematics.

Divisibility Rules from 1 to 20

Divisibility by 2

A number is divisible by 2 if its last digit is 0, 2, 4, 6, or 8 .

Example: 248, 356, and 890 are divisible by 2, but 357 isn’t.

Trick: Just check the last digit—no need for full division!

Divisibility by 3

A number is divisible by 3 if the sum of its digits is a multiple of 3.

Example: 123 → (1+2+3) = 6 (divisible by 3) ✅

Shortcut: If you get a large number, keep summing the digits until a single-digit number is obtained.

Divisibility by 4

A number is divisible by 4 if its last two digits form a number that is divisible by 4.

Example: 3128 → (28 is divisible by 4) ✅

Trick: Ignore the first digits; just check the last two!

Divisibility by 5

A number is divisible by 5 if it ends in 0 or 5 .

Example: 255, 780, and 1005 are divisible by 5.

Divisibility by 6

A number is divisible by 6 if it is divisible by both 2 and 3 .

Example: 216 → (Even number ✅ & sum of digits = 9, which is divisible by 3 ✅) → Divisible by 6 ✅

Shortcut: Apply divisibility rules of 2 and 3 together!

Divisibility by 7

Double the last digit and subtract it from the rest of the number. If the result is divisible by 7, the original number is too.

Example: 287 → (Double 7 = 14, subtract from 28 → 28 - 14 = 14, which is divisible by 7) ✅

Divisibility by 8

A number is divisible by 8 if its last three digits form a number that is divisible by 8.

Example:



5160 → (160 is divisible by 8) ✅

Divisibility by 9

A number is divisible by 9 if the sum of its digits is a multiple of 9.

Example: 729 → (7+2+9) = 18 (divisible by 9) ✅

Divisibility by 10

A number is divisible by 10 if it ends in 0.

Example: 100, 250, and 890 ✅

Divisibility by 11

Alternate sum rule—find the difference between the sum of digits at odd places and even places. If the result is 0 or divisible by 11, the number is divisible by 11.

Example: 2728 → (2+2) - (7+8) = 4 - 15 = -11 ✅

Shortcut: Works excellent for long numbers!

Divisibility by 12

A number must be divisible by both 3 and 4.

Example: 144 → (Sum of digits = 9 ✅ & last two digits = 44, divisible by 4 ✅) ✅

Divisibility by 13

Multiply the last digit by 9, subtract it from the rest. If the result is divisible by 13, so is the number.

Example: 455 → (5×9 = 45, 45 - 45 = 0) ✅

Divisibility by 14

A number must be divisible by both 2 and 7.

Example: 364 → (Even ✅ & 36 - (4×2) = 28, divisible by 7 ✅) ✅

Divisibility by 15

A number must be divisible by both 3 and 5.

Example: 225 → (Sum = 9 ✅ & ends in 5 ✅) ✅

Divisibility by 16

A number is divisible by 16 if the last four digits form a number that is divisible by 16.

Example: 5248 → (5248 is divisible by 16) ✅

Divisibility by 17





Subtract 5 times the last digit from the rest of the number. If the result is divisible by 17, so is the number.

Example: 289 → (9×5 = 45, 28 - 45 = -17) ✅

Divisibility by 18

A number must be divisible by both 2 and 9.

Example: 234 → (Even ✅ & Sum = 9 ✅) ✅

Divisibility by 19

Multiply the last digit by 2, subtract from the rest. If the result is divisible by 19, the number is too.

Example: 437 → (7×2 = 14, 43 - 14 = 29, not divisible) ❌

Divisibility by 20

A number must be divisible by both 5 and 4.

Example: 560 → (Ends in 0 ✅ & 60 is divisible by 4 ✅) ✅

Quick Tricks for Faster Calculation (Vedic Math Techniques)

- Check divisibility of large numbers quickly: Instead of summing all digits, break the number into smaller parts.
- Multiplication-based divisibility check: Instead of subtracting for 7, 13, and 17, divide in steps using nearest multiples.
- Use digit sums for 3, 9, and 11: If confused, reduce the number to a single-digit sum!

Mastering these rules will significantly speed up calculations in competitive exams like SSC, Banking, and CAT. Keep practicing with real-world examples like checking bill amounts, mobile numbers, and transaction values! ? Quiz Instructions
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