ⓘ 78 (number)

                                     

ⓘ 78 (number)

78 is:

  • a Harshad number in bases 3, 4, 5, 6, 7, 13 and 14.
  • an Erdos–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.
  • a sphenic number, having 3 distinct prime factors.
  • an abundant number with an aliquot sum of 90.
  • the dimension of the exceptional Lie group E 6 and several related objects.
  • a palindromic number in bases 5 303 5, 7 141 7, 12 66 12, 25 33 25, 38 22 38, 77 11 77 and all bases greater 78.
  • a semiperfect number, as a multiple of a perfect number.
  • the 12th triangular number.

77 and 78 form a Ruth-Aaron pair.

                                     

1. In other fields

78 is also:

  • The Rule of 78s is a method of yearly interest calculation
  • A typical tarot deck containing the 21 trump cards, the Fool and the 56 suit cards make up 78 cards
  • In reference to gramophone records, 78 refers those meant to be spun at 78 revolutions per minute. Compare: LP, ​ 33 1 ⁄ 3 and 45 rpm. 33 + 45 = 78
  • The total number of gifts in the song The Twelve Days of Christmas since 78 is the 12th triangular number