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.

## Contents

* 1 In mathematics
* 2 In science
* 3 In other fields
* 4 References

## 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 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]
* 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: 82+32+22+12, 72+42+32+22 or 62+52+42+12 (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". OEIS Foundation. https://oeis.org/A007304.
2. ↑ "Sloane's A059756 : Erdős-Woods numbers". OEIS Foundation. https://oeis.org/A059756.
3. ↑ Sloane, N. J. A., ed. "Sequence A025386 (Numbers that are the sum of 4 distinct nonzero squares in 2 or more ways.)". OEIS Foundation. https://oeis.org/A025386.
4. ↑ Sloane, N. J. A., ed. "Sequence A025378 (Numbers that are the sum of 4 distinct nonzero squares in exactly 3 ways.)". OEIS Foundation. https://oeis.org/A025378.

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