Number

540

540 is a composite number, even, a calendar year.

540 (five hundred forty) is an even 3-digit number. It is a composite number with 24 divisors, and factors as 2² × 3³ × 5. Its proper divisors sum to 1,140, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is DXL and in binary, 1000011100.

Abundant Number Arithmetic Number Decagonal Descending Digits Evil Number Harshad / Niven Heptagonal Highly Abundant Practical Number Recamán's Sequence Semiperfect Number Year

Interestingness

★ ★ ★ ★ ★

9 notable facts · grade A

528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552

less more

Historical context — 540 AD

Calendar year

Year 540 (DXL) was a leap year starting on Sunday of the Julian calendar.

Excerpt from Wikipedia (en) ↗ · Licensed CC BY-SA 4.0 Read the full article on Wikipedia →

Historical context — 540 BC

Calendar year

The year 540 BC was a year of the pre-Julian Roman calendar.

Excerpt from Wikipedia (en) ↗ · Licensed CC BY-SA 4.0 Read the full article on Wikipedia →

Year facts

Year type: Leap year
Divisible by 4 and not by 100; February has 29 days.
Days in year: 366
ISO weeks: 52
Started on: Friday
January 1, 540
Ended on: Saturday
December 31, 540
Friday the 13ths: 1
One Friday the 13th this year.
Decade: 540s
540–549
Century: 6th century
501–600
Millennium: 1st millennium
1–1000
Years ago: 1,486
1486 years before 2026.

In other calendars

Hebrew: 4300 / 4301 AM
Rosh Hashanah falls in September/October.
Chinese: Year of the zodiac:Metal zodiac:Monkey
Sexagenary cycle position 57 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 1083 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: 532 / 533 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 462 / 461 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 3
Digit sum: 9
Digit product: 0
Digital root: 9
Palindrome: No
Bit width: 10 bits
Reversed: 45
Recamán's sequence: a(1,179) = 540
Square (n²): 291,600
Cube (n³): 157,464,000
Divisor count: 24
σ(n) — sum of divisors: 1,680
φ(n) — Euler's totient: 144
Sum of prime factors: 18

Primality

Prime factorization: 2 ² × 3 ³ × 5

Nearest primes: 523 (−17) · 541 (+1)

Divisors & multiples

All divisors (24)

1 · 2 · 3 · 4 · 5 · 6 · 9 · 10 · 12 · 15 · 18 · 20 · 27 · 30 · 36 · 45 · 54 · 60 · 90 · 108 · 135 · 180 · 270 (half) · 540

Aliquot sum (sum of proper divisors): 1,140

Factor pairs (a × b = 540)

1 × 540

2 × 270

3 × 180

4 × 135

5 × 108

6 × 90

9 × 60

10 × 54

12 × 45

15 × 36

18 × 30

20 × 27

First multiples

540 · 1,080 (double) · 1,620 · 2,160 · 2,700 · 3,240 · 3,780 · 4,320 · 4,860 · 5,400

Sums & aliquot sequence

As consecutive integers: 179 + 180 + 181 106 + 107 + 108 + 109 + 110 64 + 65 + … + 71 56 + 57 + … + 64

Aliquot sequence: 540 → 1,140 → 2,220 → 4,164 → 5,580 → 11,892 → 15,884 → 16,120 → 24,200 → 37,645 → 7,535 → 2,401 → 400 → 561 → 303 → 105 → 87 — unresolved within range

Continued fraction of √n

√540 = [23; (4, 4, 1, 10, 1, 4, 4, 46)]

Period length 8 — the block in parentheses repeats forever.

Representations

In words: five hundred forty
Ordinal: 540th
Roman numeral: DXL
Binary: 1000011100
Octal: 1034
Hexadecimal: 0x21C
Base64: Ahw=
One's complement: 64,995 (16-bit)
Scientific notation: 5.4 × 10²
As a duration: 540 s = 9 minutes

In other bases

ternary (3) 202000

quaternary (4) 20130

quinary (5) 4130

senary (6) 2300

septenary (7) 1401

nonary (9) 660

undecimal (11) 451

duodecimal (12) 390

tridecimal (13) 327

tetradecimal (14) 2a8

pentadecimal (15) 260

As an angle

540° = 1 × 360° + 180°

180° ≈ 3.142 rad

Compass bearing: S (south)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹 ·
Egyptian hieroglyphic: 𓍢𓍢𓍢𓍢𓍢𓎆𓎆𓎆𓎆
Greek (Milesian): φμʹ
Mayan (base 20): 𝋡·𝋧·𝋠
Chinese: 五百四十
Chinese (financial): 伍佰肆拾

In other modern scripts

Eastern Arabic ٥٤٠ Devanagari ५४० Bengali ৫৪০ Tamil ௫௪௦ Thai ๕๔๐ Tibetan ༥༤༠ Khmer ៥៤០ Lao ໕໔໐ Burmese ၅၄၀

Digit at this position in famous constants

π — Pi (π): Digit 540 = 3
e — Euler's number (e): Digit 540 = 9
φ — Golden ratio (φ): Digit 540 = 6
√2 — Pythagoras's (√2): Digit 540 = 0
ln 2 — Natural log of 2: Digit 540 = 1
γ — Euler-Mascheroni (γ): Digit 540 = 8

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 540, here are decompositions:

17 + 523 = 540
19 + 521 = 540
31 + 509 = 540
37 + 503 = 540
41 + 499 = 540
53 + 487 = 540
61 + 479 = 540
73 + 467 = 540

Showing the first eight; more decompositions exist.

Unicode codepoint

Latin Capital Letter Yogh

U+021C

Uppercase letter (Lu)

UTF-8 encoding: C8 9C (2 bytes).

Lookup U+021C on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#00021C

RGB(0, 2, 28)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.2.28.

Address: 0.0.2.28
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.2.28

Unspecified address (0.0.0.0/8) — "this network" placeholder.

NANP area code 540

The number 540 is an active NANP area code (North American Numbering Plan).

Primary area: Roanoke / Harrisonburg
Region: Virginia
Country: United States

Most NANP area codes have multiple overlays in dense regions; the primary area listed is the historic/largest population center for this code.

Look up area code 540 ↗

Musical pitch

Heard as a frequency, 540 Hz is closest to:

Concert pitch (A4 = 440 Hz): C♯5 (554.4 Hz, -45¢ — about midway to C5)
Scientific pitch (C4 = 256 Hz): C♯5 (542.4 Hz, -8¢)
Baroque pitch (A4 = 415 Hz): D5 (554 Hz, -44¢)