Number

30

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

30 (thirty) is an even 2-digit number. It is a composite number with 8 divisors, and factors as 2 × 3 × 5. Its proper divisors sum to 42, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is XXX and in binary, 11110.

Abundant Number Arithmetic Number Cube-Free Evil Number Harshad / Niven Highly Abundant Partition Number Practical Number Preferred Number Pronic / Oblong Recamán's Sequence Semiperfect Number Sphenic Number Square Pyramidal Squarefree Year

Interestingness

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13 notable facts · grade A

18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

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Historical context — 30 AD

Calendar year

AD 30 (XXX) was a common year starting on Sunday of the Julian calendar.

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

Notable events — 30 BC

Aug 10 Cleopatra dies by suicide in Alexandria; Egypt becomes a Roman province.

Events compiled from Wikipedia ↗ · Licensed CC BY-SA 4.0

Year facts

Year type: Common year
Standard 365-day year; not divisible by 4 (or divisible by 100 but not 400).
Days in year: 365
ISO weeks: 52
Started on: Tuesday
January 1, 30
Ended on: Tuesday
December 31, 30
Friday the 13ths: 2
2 Friday the 13ths this year.
Decade: 30s
30–39
Century: 1st century
1–100
Millennium: 1st millennium
1–1000
Years ago: 1,996
1996 years before 2026.

In other calendars

Hebrew: 3790 / 3791 AM
Rosh Hashanah falls in September/October.
Chinese: Year of the zodiac:Metal zodiac:Tiger
Sexagenary cycle position 27 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 573 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: 22 / 23 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): -48 / -49 Saka
Indian national calendar; year starts in March.

Cultural significance

Christian significant

Thirty pieces of silver — Judas's payment for betraying Jesus.

Matthew 26:15.

Sourced from Wikipedia (Numerology, Chinese numerology, Gematria, and per-culture articles).

Properties

Parity: Even
Digit count: 2
Digit sum: 3
Digit product: 0
Digital root: 3
Palindrome: No
Bit width: 5 bits
Reversed: 3
Recamán's sequence: a(56) = 30
Square (n²): 900
Cube (n³): 27,000
Divisor count: 8
σ(n) — sum of divisors: 72
φ(n) — Euler's totient: 8
Sum of prime factors: 10

Primality

Prime factorization: 2 × 3 × 5

Nearest primes: 29 (−1) · 31 (+1)

Divisors & multiples

All divisors (8)

1 · 2 · 3 · 5 · 6 · 10 · 15 (half) · 30

Aliquot sum (sum of proper divisors): 42

Factor pairs (a × b = 30)

1 × 30

2 × 15

3 × 10

5 × 6

First multiples

30 · 60 (double) · 90 · 120 · 150 · 180 · 210 · 240 · 270 · 300

Sums & aliquot sequence

As consecutive integers: 9 + 10 + 11 6 + 7 + 8 + 9 4 + 5 + 6 + 7 + 8

Aliquot sequence: 30 → 42 → 54 → 66 → 78 → 90 → 144 → 259 → 45 → 33 → 15 → 9 → 4 → 3 → 1 → 0 — terminates at zero

Continued fraction of √n

√30 = [5; (2, 10)]

Period length 2 — the block in parentheses repeats forever.

Representations

In words: thirty
Ordinal: 30th
Roman numeral: XXX
Binary: 11110
Octal: 36
Hexadecimal: 0x1E
Base64: Hg==
One's complement: 225 (8-bit)
Scientific notation: 3 × 10¹

In other bases

ternary (3) 1010

quaternary (4) 132

quinary (5) 110

senary (6) 50

septenary (7) 42

nonary (9) 33

undecimal (11) 28

duodecimal (12) 26

tridecimal (13) 24

tetradecimal (14) 22

pentadecimal (15) 20

As an angle

30°

30° ≈ 0.524 rad

Compass bearing: NNE (north-northeast)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒌋𒌋
Egyptian hieroglyphic: 𓎆𓎆𓎆
Greek (Milesian): λʹ
Mayan (base 20): 𝋡·𝋪
Chinese: 三十
Chinese (financial): 參拾

In other modern scripts

Eastern Arabic ٣٠ Devanagari ३० Bengali ৩০ Tamil ௩௦ Thai ๓๐ Tibetan ༣༠ Khmer ៣០ Lao ໓໐ Burmese ၃၀

Digit at this position in famous constants

π — Pi (π): Digit 30 = 7
e — Euler's number (e): Digit 30 = 5
φ — Golden ratio (φ): Digit 30 = 6
√2 — Pythagoras's (√2): Digit 30 = 0
ln 2 — Natural log of 2: Digit 30 = 5
γ — Euler-Mascheroni (γ): Digit 30 = 8

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 30, here are decompositions:

7 + 23 = 30
11 + 19 = 30
13 + 17 = 30

ASCII character

As an ASCII codepoint, 30 is control character (0x1E). ASCII control character.

Hex color

#00001E

RGB(0, 0, 30)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.0.30.

Address: 0.0.0.30
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.0.30

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

US numbered highway

Matches numbered highway designations:

I-30 — Fort Worth, TX to Little Rock, AR.
US 30 — Atlantic City, NJ to Astoria, OR — follows the Lincoln Highway.

Interstate 30 on Wikipedia ↗ US 30 on Wikipedia ↗

Geographic coordinate

As a geographic coordinate in degrees, this matches:

30th parallel (latitude) — Passes through Egypt, Texas, northern Mexico, and central China — a notable climate boundary in many regions.

World map (equirectangular projection) — Latitude 30° — 30th parallel

Musical pitch

Heard as a frequency, 30 Hz is closest to:

Concert pitch (A4 = 440 Hz): B0 (30.9 Hz, -49¢ — about midway to A♯0)
Scientific pitch (C4 = 256 Hz): B0 (30.2 Hz, -12¢)
Baroque pitch (A4 = 415 Hz): C1 (30.8 Hz, -48¢ — about midway to B0)

(very low — many laptop and phone speakers can't reproduce it)

As a MIDI note number, 30 is F♯1 (46.2 Hz at concert pitch). (very low — many laptop and phone speakers can't reproduce it)

Atomic number

On the periodic table, atomic number 30 is Zinc (Zn) — period 4.

Zinc on Wikipedia ↗

Angle

30° is π/6 radians — the smaller angle of a 30-60-90 triangle.