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 great 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!
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