1458 (number)
1458 is the integer after 1457 and before 1459.
| ||||
|---|---|---|---|---|
| Cardinal | One thousand four hundred [and] fifty-eight | |||
| Ordinal | 1458th (one thousand four hundred fifty-eighth) | |||
| Factorization | 2 × 36 | |||
| Divisors | 1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 243, 486, 729, 1458 | |||
| Greek numeral | ,ΑΥΝΗ´ | |||
| Roman numeral | MCDLVIII | |||
| Binary | 101101100102 | |||
| Ternary | 20000003 | |||
| Senary | 104306 | |||
| Octal | 26628 | |||
| Duodecimal | A1612 | |||
| Hexadecimal | 5B216 | |||
The maximum determinant of an 11 by 11 matrix of zeroes and ones is 1458.[1]
1458 is one of three numbers which, when its base 10 digits are added together, produces a sum which, when multiplied by its reversed self, yields the original number:
- 1 + 4 + 5 + 8 = 18
- 18 × 81 = 1458
The only other non-trivial numbers with this property are 81 and 1729, as well as the trivial solutions 1 and 0. It was proven by Masahiko Fujiwara. [2]
References
- Hadamard, J. (1893), "Résolution d'une question relative aux déterminants", Bulletin des Sciences Mathématiques, 17: 240–246
- Fujiwara, M. (2005), Introduction to Truly Beautiful Mathematics, pp. 100–101
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