Number

9

9 is a composite number, odd, a calendar year.

9 (nine) is an odd 1-digit number. It is a composite number with 3 divisors, and factors as 3². It is a perfect square (3²). Written other ways, in Roman numerals it is IX and in binary, 1001.

Binary Palindrome Centered Cube Cube-Free Cullen Number Deficient Number Evil Number Flippable Harshad / Niven Kaprekar Number Lucky Number Motzkin Number Narcissistic / Armstrong Nonagonal Padovan Number Perfect Square Pernicious Number Powerful Number Recamán's Sequence Refactorable Number Self Number Semiprime Unlucky Number Year Zuckerman Number

Interestingness

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Historical context — 9 AD

First 9 years of the Common Era

The 0s began on January 1, AD 1 and ended on December 31, AD 9, covering the first nine years of the Common Era.

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

Historical context — 9 BC

Calendar year

Year 9 BC was either a common year starting on Wednesday, Thursday or Friday or a leap year starting on Thursday of the Julian calendar and a leap year starting on Monday of the Proleptic Julian calendar.

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

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: 53
Long year: contains 53 ISO weeks.
Started on: Thursday
January 1, 9
Ended on: Thursday
December 31, 9
Friday the 13ths: 3
3 Friday the 13ths this year.
Decade: 0s
0–9
Century: 1st century
1–100
Millennium: 1st millennium
1–1000
Years ago: 2,017
2017 years before 2026.

In other calendars

Hebrew: 3769 / 3770 AM
Rosh Hashanah falls in September/October.
Chinese: Year of the zodiac:Earth zodiac:Snake
Sexagenary cycle position 6 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 552 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: 1 / 2 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): -69 / -70 Saka
Indian national calendar; year starts in March.

Cultural significance

Chinese lucky

Lucky — historically associated with the emperor and longevity.

九 (jiǔ) sounds like 久 (jiǔ, "long-lasting, eternal"). The Forbidden City has 9,999 rooms.

Japanese unlucky

Avoided — pronounced "ku," the same as "suffering" or "agony" (苦).

Norse sacred

Nine worlds of the Yggdrasil cosmos; Odin hung on the world tree for nine nights.

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

Properties

Parity: Odd
Digit count: 1
Digit sum: 9
Digital root: 9
Palindrome: Yes
Bit width: 4 bits
Flips to (rotate 180°): 6
Recamán's sequence: a(14) = 9
Square (n²): 81
Cube (n³): 729
Square root (√n): 3
Divisor count: 3
σ(n) — sum of divisors: 13
φ(n) — Euler's totient: 6
Sum of prime factors: 6

Primality

Prime factorization: 3 ²

Nearest primes: 7 (−2) · 11 (+2)

Divisors & multiples

All divisors (3)

1 · 3 · 9

Aliquot sum (sum of proper divisors): 4

Factor pairs (a × b = 9)

1 × 9

3 × 3

First multiples

9 · 18 (double) · 27 · 36 · 45 · 54 · 63 · 72 · 81 · 90

Sums & aliquot sequence

As a sum of two squares: 0² + 3²

As a sum of two cubes: 1³ + 2³

As consecutive integers: 4 + 5 2 + 3 + 4

Aliquot sequence: 9 → 4 → 3 → 1 → 0 — terminates at zero

Representations

In words: nine
Ordinal: 9th
Roman numeral: IX
Binary: 1001
Octal: 11
Hexadecimal: 0x9
Base64: CQ==
One's complement: 246 (8-bit)

In other bases

ternary (3) 100

quaternary (4) 21

quinary (5) 14

senary (6) 13

septenary (7) 12

nonary (9) 10

undecimal (11) 9

duodecimal (12) 9

tridecimal (13) 9

tetradecimal (14) 9

pentadecimal (15) 9

Palindromic in base 2

Historical numeral systems

Babylonian (base 60): 𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓏺𓏺𓏺𓏺𓏺𓏺𓏺𓏺𓏺
Greek (Milesian): θʹ
Mayan (base 20): 𝋩
Chinese: 九
Chinese (financial): 玖

In other modern scripts

Eastern Arabic ٩ Devanagari ९ Bengali ৯ Tamil ௯ Thai ๙ Tibetan ༩ Khmer ៩ Lao ໙ Burmese ၉

Digit at this position in famous constants

π — Pi (π): Digit 9 = 5
e — Euler's number (e): Digit 9 = 2
φ — Golden ratio (φ): Digit 9 = 8
√2 — Pythagoras's (√2): Digit 9 = 6
ln 2 — Natural log of 2: Digit 9 = 8
γ — Euler-Mascheroni (γ): Digit 9 = 6

Also seen as

ASCII character

As an ASCII codepoint, 9 is HT (horizontal tab). ASCII control character.

Hex color

#000009

RGB(0, 0, 9)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.0.9.

Address: 0.0.0.9
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.0.9

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

Musical pitch

As a MIDI note number, 9 is A-1 (13.8 Hz at concert pitch). (below the ~20 Hz floor of human hearing — likely inaudible)

Atomic number

On the periodic table, atomic number 9 is Fluorine (F) — period 2.

Fluorine on Wikipedia ↗