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
Eastern Arabic, Kurdish, Persian, Sindhi	٥٤
Assamese & Bengali	৫৪
Chinese numeral, Japanese numeral	五十四
Devanāgarī	५४
Ge'ez	፶፬
Georgian	ნდ
Hebrew	נ"ד
Kannada	೫೪
Khmer	៥៤
Armenian	ԾԴ
Malayalam	൫൰൪
Meitei	꯵꯴
Thai	๕๔
Telugu	౫౪
Babylonian numeral	𒐐𒐘
Egyptian hieroglyph	𓎊𓏽
Mayan numeral	𝋢𝋮
Urdu numerals	۵۴
Tibetan numerals	༥༤
Korean numerals	오십사, 쉰넷
Financial kanji/hanja	五拾四, 伍拾肆

54 (fifty-four) is the natural number and positive integer following 53 and preceding 55. As a multiple of 2 but not of 4, 54 is an oddly even number and a composite number. The prime factorization of 54 contains four numbers, so it is 4-almost prime. When expressed in binary, 54 has an even number of 1s, so it is an evil number.

In mathematics

Number theory

54 as the sum of three positive squares

54 is an abundant number because the sum of its proper divisors (66), which excludes 54 as a divisor, is greater than itself. Like all multiples of 6, 54 is equal to some of its proper divisors summed together, so it is also a semiperfect number. These proper divisors can be summed in various ways to express all positive integers smaller than 54, so 54 is a practical number as well. Additionally, as an integer for which the arithmetic mean of all its positive divisors (including itself) is also an integer, 54 is an arithmetic number.

• Basic
  • Prime factorization
    • Størmer number
• Smoothness
  • A humble number
  • Evenly divides some powers of 60, including 60³, so it is a Regular number.
  • 3-smooth number

54 can be constructed mathematically in a variety of ways. It is the smallest number that can be expressed as the sum of three positive squares in more than two different ways. It can also be expressed as twice the third power of three, so it is a Leyland number. 54 can be expressed as the sum of two-or-more consecutive integers in three ways, so it has a politeness of 3. Additionally, 54 objects can be positioned to construct the vertices of a 19-sided polygon, so 54 is an enneadecagonal number and the first 19-gonal number after 19 itself. To do so, one makes an inner shell of 19 points at the regular polygon's vertices and an outer shell of 36 points where each side is 2-points-long; the two shells share one point by convention, so the total is 54.

Trigonometry

• The sine of an angle of 54 degrees is half the golden ratio. Equivalent to cos(36) and cos(π/5).
• The 54² cannot be expressed as the sum of two other squares, so the Pythagorean theorem shows 54 cannot be the hypotenuse of a triangle with integer sides; 54 is a nonhypotenuse number.
• 54 can be expressed as the area of a triangle with three rational number sides, so it is a congruent number

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

In The Hitchhiker's Guide to the Galaxy by Douglas Adams, the "Answer to the Ultimate Question of Life, the Universe, and Everything" famously was 42. Eventually, one character's attempt to divine the Ultimate Question elicited "What do you get if you multiply six by nine?" The story did not present this as the true Ultimate Question, and the mathematical answer was 54, not 42. Some readers who were trying to find a deeper meaning in the passage soon noticed a certain veracity when using base-13: the decimal expression 54 is encoded as 42 in base-13. Adams said this was a coincidence.

See also

• 45 (number) – 54 reversed

References

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