54 (number)

This article is about the number. For the years, see 54 BC and AD 54. For other uses, see 54.

← 53 54 55 →
← 50 51 52 53 54 55 56 57 58 59 → List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	fifty-four
Ordinal	54th (fifty-fourth)
Factorization	2 × 33
Divisors	1, 2, 3, 6, 9, 18, 27, 54
Greek numeral	ΝΔ´
Roman numeral	LIV, liv
Binary	1101102
Ternary	20003
Senary	1306
Octal	668
Duodecimal	4612
Hexadecimal	3616
Chinese numeral, Japanese numeral	五十四
Telugu	౫౪
Babylonian numeral	𒐐𒐘
Egyptian hieroglyph	𓎊𓏽
Mayan numeral	𝋢𝋮
Morse code	........._
ASCII value	6

54 (fifty-four; LIV) is the number following 53 and preceding 55. 54 is a natural number and a positive integer. As a multiple of 2 but not 4, 54 is an oddly even number and a composite number.

In mathematics

Number theory

54 as the sum of three positive squares

• 54 is an abundant number and a semiperfect number, like all other multiples of 6.
  • An Aliquot sum of 66
• It is twice the third power of three, 3³ + 3³ = 54, and hence is a Leyland number.
• 54 is the smallest number that can be written as the sum of three positive squares in more than two different ways: 7² + 2² + 1² = 6² + 3² + 3² = 5² + 5² + 2² = 54.
• It is a 19-gonal number,
• A humble number
• An evil number
• 4-almost prime.
• Generalized Cullen number base 3
• Practical number
• Nonhypotenuse number
• Regular number
• 3-smooth number
• Sorting number
• Størmer number
• Polydivisible number (aka Magic number)
• Polite number
• Arithmetic number
• Congruent number

Trigonometry

• The sine of an angle of 54 degrees is half the golden ratio.

Recreational mathematics

54 is divisible by the sum of its digits in 21 bases, meaning it is a Harshad number in those bases. For example, in base 10, the sum of 54's digits (5 and 4), is 9, which is a divisor of 54, so 54 is a Harshad number in base 10.

List of basic calculations

Multiplication	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
54 × x	54	108	162	216	270	324	378	432	486	540	594	648	702	756	810	918	972	1026	1080	1134

Division	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
54 ÷ x	54	27	18	13.5	10.8	9	7.714285	6.75	6	5.4	4.90	4.5	4.153846	3.857142	3.6
x ÷ 54	0.01851	0.037	0.05	0.074	0.0925	0.1	0.1296	0.148	0.16	0.185	0.2037	0.2	0.2407	0.259	0.27

Exponentiation	1	2	3	4	5
54x	54	2916	157464	8503056	459165024
x54	1	18014398509481984	58149737003040059690390169	324518553658426726783156020576256	55511151231257827021181583404541015625
${\sqrt[{x}]{54}}$	54	7.34846...	3.77976...	2.71080...	2.22064...

Because 54 is a multiple of 2 but not a square number, its square root is irrational.

In literature

A famous joke from The Hitchhiker's Guide to the Galaxy by Douglas Adams concerned the "Answer to the Ultimate Question of Life, the Universe, and Everything," which was 42. Eventually, one character's attempt to divine the Ultimate Question elicited "What do you get if you multiply six by nine?" The mathematical answer is 54, and the story explained the discrepancy. Some readers who were trying to find a deeper meaning in the passage soon noticed a certain veracity when using base-13; 6₁₀ × 9₁₀ = 54₁₀, which can be expressed as 42₁₃ (i.e. the decimal expression 54 is encoded as 42 in base-13). When confronted with this, Adams claimed that it was a mere coincidence, stating that "I may be a sorry case, but I don't write jokes in base 13."

See also

• 45 (number) – 54 reversed

References

Genji-mon, the traditional symbols that represent the 54 chapters of The Tale of Genji