78 (number)

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Short description: Natural number
← 77 78 79 →
Cardinalseventy-eight
Ordinal78th
(seventy-eighth)
Factorization2 × 3 × 13
Divisors1, 2, 3, 6, 13, 26, 39, 78
Greek numeralΟΗ´
Roman numeralLXXVIII
Binary10011102
Ternary22203
Quaternary10324
Quinary3035
Senary2106
Octal1168
Duodecimal6612
Hexadecimal4E16
Vigesimal3I20
Base 362636

78 (seventy-eight) is the natural number following 77 and followed by 79.

In mathematics

78 as the sum of four distinct nonzero squares

78 is:

  • the 4th discrete tri-prime; or also termed Sphenic number, and the 4th of the form (2.3.r).[1]
  • an abundant number with an aliquot sum of 90.
  • a semiperfect number, as a multiple of a perfect number.
  • the 12th triangular number.
  • a palindromic number in bases 5 (3035), 7 (1417), 12 (6612), 25 (3325), and 38 (2238).
  • a Harshad number in bases 3, 4, 5, 6, 7, 13 and 14.
  • an Erdős–Woods number, since it is possible to find sequences of 78 consecutive integers such that each inner member shares a factor with either the first or the last member.[2]
  • the dimension of the exceptional Lie group E6 and several related objects.
  • the smallest number that can be expressed as the sum of four distinct nonzero squares in more than one way: [math]\displaystyle{ 8^2+3^2+2^2+1^2 }[/math], [math]\displaystyle{ 7^2+4^2+3^2+2^2 }[/math] or [math]\displaystyle{ 6^2+5^2+4^2+1^2 }[/math] (see image).[3][4]

77 and 78 form a Ruth–Aaron pair.

In science

In other fields

See also: List of highways numbered 78

78 is also:

  • In reference to gramophone records, 78 refers those meant to be spun at 78 revolutions per minute. Compare: LP, ​33 13 and 45 rpm. 33 + 45 = 78
  • A typical tarot deck containing the 21 trump cards, the Fool and the 56 suit cards make up 78 cards
  • The Rule of 78s is a method of yearly interest calculation
  • The number used by Martin Truex Jr. and Furniture Row Racing to win the 2017 Monster Energy NASCAR Cup Series championship and 2016 Coca-Cola 600. The team and driver Regan Smith also won the 2011 Showtime Southern 500 with 78. The number is now used by owner-driver B.J. McLeod for Live Fast Motorsports.

References