Divisibility Test
Check if a number is divisible by integers from 1 to 12 with explanations of divisibility rules.
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Divisibility by 1–12
Divisible vs Not
📐 Step-by-Step Breakdown
For educational and informational purposes only. Verify with a qualified professional.
📋 Key Takeaways
- • 2: last digit even
- • 3: sum of digits divisible by 3
- • 4: last two digits divisible by 4
- • 5: last digit 0 or 5
- • 6: divisible by both 2 and 3
- • 9: sum of digits divisible by 9
- • 10: last digit 0
💡 Did You Know?
📖 How It Works
Divisibility rules are shortcuts to check if a number divides another without performing full division. Each divisor from 2 to 12 has a rule based on digit patterns.
📝 Worked Example: 144
÷2: Last digit 4 (even) ✓
÷3: 1+4+4 = 9, 9÷3 ✓
÷4: Last two 44, 44÷4 ✓
÷6: ÷2 and ÷3 ✓
🎯 Expert Tips
- Combine rules: 6 = 2 and 3, 12 = 3 and 4
- Use prime factorization to find all divisors
- Sum of digits for 3 and 9
- Last-digit rules for 2, 5, 10
📊 Reference Table
| Divisor | Rule |
|---|---|
| 2 | Last digit even |
| 3 | Sum of digits ÷ 3 |
| 4 | Last 2 digits ÷ 4 |
| 5 | Last digit 0 or 5 |
| 6 | ÷2 and ÷3 |
| 9 | Sum of digits ÷ 9 |
| 10 | Last digit 0 |
| 11 | Alternating sum ÷ 11 |
| 12 | ÷3 and ÷4 |
❓ FAQ
How to check divisibility by 7?
Double the last digit, subtract from the rest. Repeat until small enough.
What about 11?
Alternating sum of digits (1st−2nd+3rd−...) divisible by 11.
Why does sum of digits work for 3?
10 ≡ 1 (mod 3), so 10^n ≡ 1, hence the number ≡ sum of digits (mod 3).
What is 2520?
Smallest number divisible by 1 through 10 (LCM of 1..10).
How to find all divisors?
Use prime factorization. All divisors are products of prime factors.
Is 0 divisible by any number?
Yes. 0 ÷ n = 0 for any n ≠ 0.
⚠️ Disclaimer: Results are for educational purposes.
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