78 (number)

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

← 77 79 → 78
← 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)
Numeral system	78
Factorization	$2 \cdot 3 \cdot 13$
Divisors	1, 2, 3, 6, 13, 26, 39, 78
Roman numeral	LXXVIII
Binary	10011102
Octal	1168
Duodecimal	6612
Hexadecimal	4E16

In mathematics

78 is a triangular number, and its factorization makes it a sphenic number. As a multiple of a perfect number, 78 is itself a semiperfect number.

77 and 78 form a Ruth-Aaron pair under the second definition in which repeated prime factors are counted as often as they occur.

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, 78 is an Erdős–Woods number.

Karl A. Dahlke proved in 1989 that 78 heptominos of this shape ( ), at a minimum, are required to fill a rectangle.

In science

• The atomic number of platinum
• The number of chromosomes in canine DNA^[1]

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 total number of gifts in the song The Twelve Days of Christmas (since 78 is the 12th triangular number)
• The number of lines that make up Metatron's Cube^{[citation needed]}
• The Rule of 78s is a method of yearly interest calculation^{[citation needed]}
• Municipal Okrug 78, a municipal okrug of Tsentralny District of St. Petersburg, Russia

References

1. ^ "Both wolves and dogs possess 78 chromosomes." Handbook of Applied Dog Behavior and Training by Steven R. Lindsay, Wiley-Blackwell (2000) p. 11