Guide

Divisibility Rules From 2 to 11 With Examples

The rules to tell whether a number is divisible by 2, 3, 4, 5, 6, 8, 9, 10 and 11 without dividing, with worked examples, a sample table and a trick to remember them.

By Polarzinho · October 20, 2026

In Trimora, the tower gets a wider terrace every eight floors. Which floors are those? The ones divisible by 8: 8, 16, 24, 32, 40 and 48. You can find out without dividing, using divisibility rules.

Here are the rules from 2 to 11, with worked examples. All of them were checked against real division, from 1 to 5,000.

Play Trimora

What is divisibility?

A number is divisible by another when the division comes out even, with no remainder. Divisibility rules are quick tests that tell you if that happens, without dividing.

The rules

By 2: the last digit is even (0, 2, 4, 6 or 8). Example: 348.
By 3: the sum of the digits is divisible by 3. Example: 48, because 4 + 8 = 12.
By 4: the last two digits form a number divisible by 4. Example: 316, because 16 ÷ 4 = 4.
By 5: it ends in 0 or 5. Example: 725.
By 6: it is divisible by both 2 and 3. Example: 48.
By 8: the last three digits form a number divisible by 8. Example: 1,048, because 48 ÷ 8 = 6.
By 9: the sum of the digits is divisible by 9. Example: 729, because 7 + 2 + 9 = 18.
By 10: it ends in 0. Example: 340.
By 11: add the digits in alternating positions, subtract the two sums, and the result must be 0 or a multiple of 11. Example: 121, because 1 + 1 − 2 = 0.

Sample table

Which numbers from 2 to 11 each one is divisible by:

48: 2, 3, 4, 6, 8
25: 5
144: 2, 3, 4, 6, 8, 9
121: 11

A trick to remember them

Anything ending in an even digit is divisible by 2.
The sum of the digits rules 3 and 9.
6 is "2 + 3": it has to pass both tests.
4 and 8 only look at the end of the number: the last two or three digits.

Divisibility and the Trimora floors

In Trimora you stack slabs that slide over the tower, and every eight floors the tower gets a wider terrace. By the rule of 8, floor 48 is one of those terraces.