78 (number)

78 (seventy-eight) is the natural number following 77 and followed by 79.

← 77 78 79 →
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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
Octal	1168
Duodecimal	6612
Hexadecimal	4E16

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), 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

• 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 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

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.