78 (number)

Short description: Natural 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
Greek numeral	ΟΗ´
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 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).
• 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.
• 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).

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 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.