Number

516

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

516 (five hundred sixteen) is an even 3-digit number. It is a composite number with 12 divisors, and factors as 2² × 3 × 43. Its proper divisors sum to 716, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is DXVI and in binary, 1000000100.

Abundant Number Cube-Free Evil Number Harshad / Niven Moran Number Pernicious Number Recamán's Sequence Refactorable Number Semiperfect Number Year

Interestingness

★ ★ ★ ★ ☆

6 notable facts · grade B

504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528

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Historical context — 516 AD

Calendar year

Year 516 (DXVI) was a leap year starting on Friday of the Julian calendar.

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

Historical context — 516 BC

Calendar year

The year 516 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: 53
Long year: contains 53 ISO weeks.
Started on: Wednesday
January 1, 516
Ended on: Thursday
December 31, 516
Friday the 13ths: 2
2 Friday the 13ths this year.
Decade: 510s
510–519
Century: 6th century
501–600
Millennium: 1st millennium
1–1000
Years ago: 1,510
1510 years before 2026.

In other calendars

Hebrew: 4276 / 4277 AM
Rosh Hashanah falls in September/October.
Chinese: Year of the zodiac:Fire zodiac:Monkey
Sexagenary cycle position 33 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 1059 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: 508 / 509 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 438 / 437 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 3
Digit sum: 12
Digit product: 30
Digital root: 3
Palindrome: No
Bit width: 10 bits
Reversed: 615
Recamán's sequence: a(1,227) = 516
Square (n²): 266,256
Cube (n³): 137,388,096
Divisor count: 12
σ(n) — sum of divisors: 1,232
φ(n) — Euler's totient: 168
Sum of prime factors: 50

Primality

Prime factorization: 2 ² × 3 × 43

Nearest primes: 509 (−7) · 521 (+5)

Divisors & multiples

All divisors (12)

1 · 2 · 3 · 4 · 6 · 12 · 43 · 86 · 129 · 172 · 258 (half) · 516

Aliquot sum (sum of proper divisors): 716

Factor pairs (a × b = 516)

1 × 516

2 × 258

3 × 172

4 × 129

6 × 86

12 × 43

First multiples

516 · 1,032 (double) · 1,548 · 2,064 · 2,580 · 3,096 · 3,612 · 4,128 · 4,644 · 5,160

Sums & aliquot sequence

As consecutive integers: 171 + 172 + 173 61 + 62 + … + 68 10 + 11 + … + 33

Aliquot sequence: 516 → 716 → 544 → 590 → 490 → 536 → 484 → 447 → 153 → 81 → 40 → 50 → 43 → 1 → 0 — terminates at zero

Continued fraction of √n

√516 = [22; (1, 2, 1, 1, 14, 1, 1, 2, 1, 44)]

Period length 10 — the block in parentheses repeats forever.

Representations

In words: five hundred sixteen
Ordinal: 516th
Roman numeral: DXVI
Binary: 1000000100
Octal: 1004
Hexadecimal: 0x204
Base64: AgQ=
One's complement: 65,019 (16-bit)
Scientific notation: 5.16 × 10²
As a duration: 516 s = 8 minutes, 36 seconds

In other bases

ternary (3) 201010

quaternary (4) 20010

quinary (5) 4031

senary (6) 2220

septenary (7) 1335

nonary (9) 633

undecimal (11) 42a

duodecimal (12) 370

tridecimal (13) 309

tetradecimal (14) 28c

pentadecimal (15) 246

As an angle

516° = 1 × 360° + 156°

156° ≈ 2.723 rad

Compass bearing: SSE (south-southeast)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓍢𓍢𓍢𓍢𓍢𓎆𓏺𓏺𓏺𓏺𓏺𓏺
Greek (Milesian): φιϛʹ
Mayan (base 20): 𝋡·𝋥·𝋰
Chinese: 五百一十六
Chinese (financial): 伍佰壹拾陸

In other modern scripts

Eastern Arabic ٥١٦ Devanagari ५१६ Bengali ৫১৬ Tamil ௫௧௬ Thai ๕๑๖ Tibetan ༥༡༦ Khmer ៥១៦ Lao ໕໑໖ Burmese ၅၁၆

Digit at this position in famous constants

π — Pi (π): Digit 516 = 5
e — Euler's number (e): Digit 516 = 9
φ — Golden ratio (φ): Digit 516 = 5
√2 — Pythagoras's (√2): Digit 516 = 4
ln 2 — Natural log of 2: Digit 516 = 4
γ — Euler-Mascheroni (γ): Digit 516 = 2

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 516, here are decompositions:

7 + 509 = 516
13 + 503 = 516
17 + 499 = 516
29 + 487 = 516
37 + 479 = 516
53 + 463 = 516
59 + 457 = 516
67 + 449 = 516

Showing the first eight; more decompositions exist.

Unicode codepoint

Latin Capital Letter E With Double Grave

U+0204

Uppercase letter (Lu)

UTF-8 encoding: C8 84 (2 bytes).

Lookup U+0204 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#000204

RGB(0, 2, 4)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.2.4.

Address: 0.0.2.4
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.2.4

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

NANP area code 516

The number 516 is an active NANP area code (North American Numbering Plan).

Primary area: Nassau County
Region: New York
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 516 ↗

Musical pitch

Heard as a frequency, 516 Hz is closest to:

Concert pitch (A4 = 440 Hz): C5 (523.3 Hz, -24¢)
Scientific pitch (C4 = 256 Hz): C5 (512 Hz, +13¢)
Baroque pitch (A4 = 415 Hz): C♯5 (522.9 Hz, -23¢)