78 (number)

← 77 78 79 →
← 70 71 72 73 74 75 76 77 78 79 → List of numbers — Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	seventy-eight
Ordinal	78th (seventy-eighth)
Factorization	2 × 3 × 13
Divisors	1, 2, 3, 6, 13, 26, 39, 78
Roman numeral	LXXVIII
Binary	10011102
Ternary	22203
Quaternary	10324
Quinary	3035
Senary	2106
Octal	1168
Duodecimal	6612
Hexadecimal	4E16
Vigesimal	3I20
Base 36	2636

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.