1458 (number)

From HandWiki
Short description: Natural number
← 1457 1458 1459 →
CardinalOne thousand four hundred [and] fifty-eight
Ordinal1458th
(one thousand four hundred fifty-eighth)
Factorization2 × 36
Divisors1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 243, 486, 729, 1458
Greek numeral,ΑΥΝΗ´
Roman numeralMCDLVIII
Binary101101100102
Ternary20000003
Quaternary1123024
Quinary213135
Senary104306
Octal26628
DuodecimalA1612
Hexadecimal5B216
Vigesimal3CI20
Base 3614I36

1458 is the integer after 1457 and before 1459.

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

  1. Hadamard, J. (1893), "Résolution d'une question relative aux déterminants", Bulletin des Sciences Mathématiques 17: 240–246 
  2. Fujiwara, M. (2005), Introduction to Truly Beautiful Mathematics, pp. 100–101