78 (number)

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

In mathematics

78 is:

• the dimension of the exceptional Lie group E₆ and several related objects.
• a sphenic number, having 3 distinct prime factors.^[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]

77 and 78 form a Ruth-Aaron pair.

In science

• The atomic number of platinum.

In other fields

78 is also:

• 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
• A typical tarot deck containing the 21 trump cards, the Fool and the 56 suit cards make up 78 cards
• The total number of gifts in the song The Twelve Days of Christmas (since 78 is the 12th triangular number)
• The Rule of 78s is a method of yearly interest calculation
• Municipal Okrug 78, a municipal okrug of Tsentralny District of St. Petersburg, Russia
• NASCAR driver Martin Truex Jr. currently drives the No. 78 Toyota Camry in the NASCAR Sprint Cup Series.

References

1. ↑ "Sloane's A007304 : Sphenic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29. 
2. ↑ "Sloane's A059756 : Erdős-Woods numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.