Divisibility Rules Calculator
Test a number against the divisibility rules for 2 to 12 and see the working for each: digit sums, last digits, the alternating sum for 11 and the doubling rule for 7.
About the Divisibility Rules Calculator
A divisibility rule tells you whether one number divides another without doing the division. For 3 and 9 you add the digits; for 4 and 8 you look at the last two or three digits; for 11 you subtract the sums of alternate digits; for 6 and 12 you combine two rules.
Every answer here is also checked by real division.
The formula
3 | n ⇔ 3 | (sum of digits); 11 | n ⇔ 11 | (alternating digit sum)
Worked example
Is 4752 divisible by 11?
- From the right: 2 + 7 = 9 and 5 + 4 = 9
- 9 − 9 = 0, so yes: 4752 = 11 × 432
Questions people ask
Why does the digit-sum rule work?
10 leaves remainder 1 when divided by 3 or 9, so every power of 10 does too; the number and its digit sum leave the same remainder.
Is there a rule for 7?
Yes: double the last digit and subtract it from the rest, and repeat. 343 → 34 − 6 = 28, a multiple of 7.