The divisibility rule of 8 states: A number is divisible by 8 if its last three digits (hundreds, tens, units) form a number that is divisible by 8. For numbers with fewer than three digits, check the number itself.
Divisibility rule of 8: last 3 digits divisible by 8 → whole number divisible by 8.
Why 3 digits: because 1000 ÷ 8 = 125 (exact), so thousands place and above don't matter.
Example: 2048 → 048 = 48 ÷ 8 = 6 ✓ divisible.
Example: 1234 → 234 ÷ 8 = 29.25 ✗ not divisible.
For 2-digit numbers: check the number itself (16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96).
Divisibility rule of 4: last 2 digits (pattern: 4 = 2² = last 2 digits; 8 = 2³ = last 3 digits).
The Rule: A number is divisible by 8 if its last 3 digits are divisible by 8.
Why 3 digits? Because 1000 is divisible by 8 (1000 ÷ 8 = 125), so any thousands or higher portion is automatically divisible by 8. Only the last 3 digits matter.
Examples: • 2,048: last 3 digits = 048 = 48; 48 ÷ 8 = 6 ✓ → divisible by 8 • 1,512: last 3 digits = 512; 512 ÷ 8 = 64 ✓ → divisible by 8 • 7,224: last 3 digits = 224; 224 ÷ 8 = 28 ✓ → divisible by 8 • 1,234: last 3 digits = 234; 234 ÷ 8 = 29.25 ✗ → NOT divisible by 8 • 3,006: last 3 digits = 006 = 6; 6 ÷ 8 = 0.75 ✗ → NOT divisible by 8 • 4,000: last 3 digits = 000 = 0; 0 ÷ 8 = 0 ✓ → divisible by 8
For 2-digit or 1-digit numbers: • 16: 16 ÷ 8 = 2 ✓ • 24: 24 ÷ 8 = 3 ✓ • 40: 40 ÷ 8 = 5 ✓ • 56: 56 ÷ 8 = 7 ✓ • 48: 48 ÷ 8 = 6 ✓ • 100: not divisible (100 ÷ 8 = 12.5)
10 Practice Problems:
All Divisibility Rules Quick Reference:
| Divisor | Rule |
|---|---|
| 2 | Last digit is 0, 2, 4, 6, or 8 |
| 3 | Sum of digits divisible by 3 |
| 4 | Last 2 digits divisible by 4 |
| 5 | Last digit is 0 or 5 |
| 6 | Divisible by both 2 and 3 |
| 7 | Complex — (2×last digit subtracted from rest) |
| 8 | Last 3 digits divisible by 8 |
| 9 | Sum of digits divisible by 9 |
| 10 | Last digit is 0 |
| 11 | Alternating sum of digits divisible by 11 |
A number is divisible by 8 if its last three digits form a number that is divisible by 8. For example: 1512 → last 3 digits = 512 → 512 ÷ 8 = 64 → divisible. 1234 → last 3 digits = 234 → 234 ÷ 8 = 29.25 → not divisible. For numbers under 1000, check the number directly.
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