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
Greek numeral	ΟΗ´
Roman numeral	LXXVIII
Binary	10011102
Ternary	22203
Senary	2106
Octal	1168
Duodecimal	6612
Hexadecimal	4E16

78 (seventy-eight) is the natural number following 77 and preceding 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 33; within an aliquot sequence of nine composite numbers (78, 90,144,259,45,33,15,9,4,3,1,0) to the Prime in the 3-aliquot tree.
• 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: ${\displaystyle 8^{2}+3^{2}+2^{2}+1^{2}}$, ${\displaystyle 7^{2}+4^{2}+3^{2}+2^{2}}$ or ${\displaystyle 6^{2}+5^{2}+4^{2}+1^{2}}$ (see image). ^{[3] [4]}

77 and 78 form a Ruth–Aaron pair.

In science

• The atomic number of platinum.

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 +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.

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.
3. Sloane, N. J. A. (ed.). "SequenceA025386(Numbers that are the sum of 4 distinct nonzero squares in 2 or more ways.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
4. Sloane, N. J. A. (ed.). "SequenceA025378(Numbers that are the sum of 4 distinct nonzero squares in exactly 3 ways.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.