78 (number)
78 (number)
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|---|---|---|---|---|
| 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[edit]
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), 38 (2238), 77 (1177) and all bases greater 78.
- 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[edit]
- The atomic number of platinum.
In other fields[edit]
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 on the twelfth day 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
References[edit]
- ^ "Sloane's A007304 : Sphenic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
- ^ "Sloane's A059756 : Erdős-Woods numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
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