Base 30
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Base 30 or trigesimal is a positional numeral system using 30 as the radix. Digits in this base can be represented using the Arabic numerals 0-9 and the Latin letters A-T.
From a mathematical viewpoint, 30 is a convenient choice for a base in that it is divisible by the three smallest prime numbers (2, 3, and 5) and by their multiples 6, 10, and 15 — many vulgar fractions are easily expressed in base 30. On the other hand, base 30 has poor radix economy, and it shares the problem with base 60 of its radix falling between twin primes, resulting in few recurring fractions having short periods.
| Decimal | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Base 30 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E |
| Decimal | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 |
| Base 30 | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T |
| Decimal base Prime factors of the base: 2, 5 |
Base 30 Prime factors of the base: 2, 3, 5 |
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| Fraction | Prime factors of the denominator |
Positional representation | Positional representation | Prime factors of the denominator |
Fraction |
| 1/2 | 2 | 0.5 | 0.F | 2 | 1/2 |
| 1/3 | 3 | 0.3333... = 0.3 | 0.A | 3 | 1/3 |
| 1/4 | 2 | 0.25 | 0.7F | 2 | 1/4 |
| 1/5 | 5 | 0.2 | 0.6 | 5 | 1/5 |
| 1/6 | 2, 3 | 0.16 | 0.5 | 2, 3 | 1/6 |
| 1/7 | 7 | 0.142857 | 0.48H | 7 | 1/7 |
| 1/8 | 2 | 0.125 | 0.3MF | 2 | 1/8 |
| 1/9 | 3 | 0.1 | 0.3A | 3 | 1/9 |
| 1/10 | 2, 5 | 0.1 | 0.3 | 2, 5 | 1/A |
| 1/11 | 11 | 0.09 | 0.2LOGAR85DJ | B | 1/B |
| 1/12 | 2, 3 | 0.083 | 0.2F | 2, 3 | 1/C |
| 1/13 | 13 | 0.076923 | 0.296RKN | D | 1/D |
| 1/14 | 2, 7 | 0.0714285 | 0.248H | 2, 7 | 1/E |
| 1/15 | 3, 5 | 0.06 | 0.2 | 3, 5 | 1/F |
| 1/16 | 2 | 0.0625 | 0.1Q7F | 2 | 1/G |
| 1/17 | 17 | 0.0588235294117647 | 0.1MS7 | H | 1/H |
| 1/18 | 2, 3 | 0.05 | 0.1K | 2, 3 | 1/I |
| 1/19 | 19 | 0.052631578947368421 | 0.1HB | J | 1/J |
| 1/20 | 2, 5 | 0.05 | 0.1F | 2, 5 | 1/K |
| 1/21 | 3, 7 | 0.047619 | 0.1CPL | 3, 7 | 1/L |
| 1/22 | 2, 11 | 0.045 | 0.1AR85DJ2LOG | 2, B | 1/M |
| 1/23 | 23 | 0.0434782608695652173913 | 0.193RBM56FJGSKQ2I7ONEAD | N | 1/N |
| 1/24 | 2, 3 | 0.0416 | 0.17F | 2, 3 | 1/O |
| 1/25 | 5 | 0.04 | 0.16 | 5 | 1/P |
| 1/26 | 2, 13 | 0.0384615 | 0.14IDPBG | 2, D | 1/Q |
| 1/27 | 3 | 0.037 | 0.13A | 3 | 1/R |
| 1/28 | 2, 7 | 0.03571428 | 0.1248H | 2, 7 | 1/S |
| 1/29 | 29 | 0.0344827586206896551724137931 | 0.1 | T | 1/T |
| 1/30 | 2, 3, 5 | 0.03 | 0.1 | 2, 3, 5 | 1/10 |
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