11. Vigesimal Divisibility Tests
These allow a reader to check divisibility without dividing. They are base-20-internal: only the number's own digits are examined.
| Divisor | Test | Type |
|---|---|---|
| 2 | Units digit is even (0, 2, 4, 6, 8, 10, 12, 14, 16, 18) — its body is 0B, 2B or 4B with an even flag level, or 1B/3B with an odd one | Last-digit test |
| 3 | Alternating digit sum is divisible by 3 | Alternating-sum test |
| 4 | Units digit is one of {0, 4, 8, 12, 16} | Last-digit test |
| 5 | Units digit is 0, 5, 10, or 15 — its body contribution is zero (0B) | Last-digit test |
| 6 | Divisible by both 2 and 3 | Composite |
| 7 | Alternating digit sum is divisible by 7 | Alternating-sum test |
| 10 | Units digit is 0 or 10 | Last-digit test |
| 11 | From right to left, multiply digits by repeating weights 1, −2, 4, 3, 5, 1, … and add. The sum must be divisible by 11. | Weighted-sum test |
| 19 | Digital root (repeated digit sum) is divisible by 19 | Digit-sum test |
| 20 | Units digit is 0 | Last-digit test |
− + =
Notes: - The ÷5 test is visually immediate in Ńdẹ́bẹ́: look at the units glyph — a zero-valued body means divisible by 5. The complete numerals 5, 10, and 15 retain their plain bodies; do not replace them with isolated flags. - The alternating-sum tests for 3 and 7 work because 3 × 7 = 21 = one more than the base (as 11 in base 10). - The digital-root test for 19 works because 19 = one less than the base (as 9 in base 10).