Quick Divisibility Rules
Check divisibility without doing the division.
÷3,9: digit sum · ÷4: last two digits · ÷11: alternating sum
1How it works
Simple digit tests tell you instantly whether a number is divisible by 3, 4, 9 or 11 — handy for simplifying fractions and eliminating options.
2How to apply (in seconds)
- By 3 or 9: add all digits; if the sum is divisible by 3 (or 9), so is the number.
- By 4: check if the last two digits form a multiple of 4.
- By 11: take the difference of the sums of alternate digits; 0 or a multiple of 11 means it divides.
3Worked examples
Example 1 Worked solution
Q. Is 8514 divisible by 9?
- Digit sum = 8 + 5 + 1 + 4 = 18.
- 18 is divisible by 9.
✓ Yes
4When to use it
- ✦Simplifying fractions and ruling out wrong options.
- ✦HCF, LCM and number-system questions.
5Cautions & tips
- !Divisible by 6 means divisible by both 2 and 3.