Divisibility Calculator with Rules
Type a number (even 30 digits long) and a divisor. You get the remainder, the quotient and the divisibility rule worked out.
- Nothing you type is stored
- Free
- No signup
Remainder
0
Divisible- Quotient
- 41,152
- Next multiple
- 1,23,456
Show working
- Σ = 1 + 2 + 3 + 4 + 5 + 6 = 21; 21 ÷ 3 → ✓
- 1,23,456 = 3 × 41,152 + 0
Check by 2–12 and 25
| By | Divisible? | Rule check |
|---|---|---|
| 2 | ✓ | …6 → 0, 2, 4, 6, 8 ✓ |
| 3 | ✓ | Σ = 1 + 2 + 3 + 4 + 5 + 6 = 21; 21 ÷ 3 → ✓ |
| 4 | ✓ | …56 ÷ 4 → ✓ |
| 5 | ✗ | …6 → ✗ |
| 6 | ✓ | ÷ 2 ✓, ÷ 3 ✓ |
| 7 | ✗ | 12345 − 2 × 6 = 12333; 1233 − 2 × 3 = 1227; 122 − 2 × 7 = 108; 10 − 2 × 8 = -6; 6 ÷ 7 → ✗ |
| 8 | ✓ | …456 ÷ 8 → ✓ |
| 9 | ✗ | Σ = 1 + 2 + 3 + 4 + 5 + 6 = 21; 21 ÷ 9 → 3 ✗ |
| 10 | ✗ | …6 → ✗ |
| 11 | ✗ | 12 − 9 = 3; 3 ÷ 11 → ✗ |
| 12 | ✓ | ÷ 3 ✓, ÷ 4 ✓ |
| 25 | ✗ | …56 → ✗ |
How to use
- Type the number.
- Type the number to divide by.
- Read Divisible or Not divisible, then check the rule table for 2 to 12 and 25.
Good to know
Quick rules: 2 – last digit even; 3 – digit sum divisible by 3; 4 – last two digits divisible by 4; 5 – ends in 0 or 5; 6 – divisible by 2 and 3; 8 – last three digits divisible by 8; 9 – digit sum divisible by 9; 10 – ends in 0; 11 – (sum of digits in odd places) − (sum in even places) is 0 or a multiple of 11; 12 – divisible by 3 and 4; 25 – ends in 00, 25, 50 or 75.
For 7: double the last digit and subtract it from the rest; repeat until the number is small. 343 → 34 − 6 = 28, which is 4 × 7, so 343 is divisible by 7. The table shows each rule worked on your number, so you can learn the rules by checking them.
The calculator uses exact whole-number arithmetic, so very long numbers (like a 20-digit roll number or a bank reference) are handled without rounding. These rules are part of NCERT Class 6 'Playing with Numbers' and appear in most aptitude tests.
Questions
How do I check divisibility by 3?
Add the digits. If the sum is divisible by 3, so is the number. 123456: 1 + 2 + 3 + 4 + 5 + 6 = 21, divisible by 3.
What is the divisibility rule of 11?
Find the difference between the sums of alternate digits. 1331: (1 + 3) − (3 + 1) = 0, so it is divisible by 11.
What is the rule for 7?
Double the last digit and subtract it from the number formed by the other digits. Repeat. If you reach 0, 7, 14, −7… it is divisible.
If a number is divisible by 4 and 6, is it divisible by 24?
Not always. 12 is divisible by 4 and 6 but not 24. You need co-prime divisors: 3 and 8 together do give 24.
What is the remainder?
What's left after dividing as many whole times as possible. 23 ÷ 5 = 4 remainder 3, because 5 × 4 + 3 = 23.