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 ✅

Divisibilit

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