Number

21

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

21 (twenty-one) is an odd 2-digit number. It is a composite number with 4 divisors, and factors as 3 × 7. It is the sixth triangular number and a Fibonacci number. Written other ways, in Roman numerals it is XXI and in binary, 10101.

Arithmetic Number Binary Palindrome Cube-Free Deficient Number Fibonacci Harshad / Niven Jacobsthal Number Moran Number Motzkin Number Octagonal Odious Number Padovan Number Pernicious Number Recamán's Sequence Semiprime Squarefree Triangular Year

Interestingness

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14 notable facts · grade A

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Historical context — 21 AD

Calendar year

AD 21 (XXI) was a common year starting on Wednesday of the Julian calendar.

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

Historical context — 21 BC

Calendar year

Year 21 BC was either a common year starting on Monday, Tuesday or Wednesday or a leap year starting on Tuesday of the Julian calendar and a leap year starting on Sunday 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: 52
Started on: Friday
January 1, 21
Ended on: Friday
December 31, 21
Friday the 13ths: 1
One Friday the 13th this year.
Decade: 20s
20–29
Century: 1st century
1–100
Millennium: 1st millennium
1–1000
Years ago: 2,005
2005 years before 2026.

In other calendars

Hebrew: 3781 / 3782 AM
Rosh Hashanah falls in September/October.
Chinese: Year of the zodiac:Metal zodiac:Snake
Sexagenary cycle position 18 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 564 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: 13 / 14 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): -57 / -58 Saka
Indian national calendar; year starts in March.

Cultural significance

American significant

Legal age of adulthood for alcohol; target score in blackjack.

21st Amendment; 21 = blackjack.

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

Properties

Parity: Odd
Digit count: 2
Digit sum: 3
Digit product: 2
Digital root: 3
Palindrome: No
Bit width: 5 bits
Reversed: 12
Recamán's sequence: a(9) = 21
Square (n²): 441
Cube (n³): 9,261
Divisor count: 4
σ(n) — sum of divisors: 32
φ(n) — Euler's totient: 12
Sum of prime factors: 10

Primality

Prime factorization: 3 × 7

Nearest primes: 19 (−2) · 23 (+2)

Divisors & multiples

All divisors (4)

1 · 3 · 7 · 21

Aliquot sum (sum of proper divisors): 11

Factor pairs (a × b = 21)

1 × 21

3 × 7

First multiples

21 · 42 (double) · 63 · 84 · 105 · 126 · 147 · 168 · 189 · 210

Sums & aliquot sequence

As consecutive integers: 10 + 11 6 + 7 + 8 1 + 2 + 3 + 4 + 5 + 6

Aliquot sequence: 21 → 11 → 1 → 0 — terminates at zero

Continued fraction of √n

√21 = [4; (1, 1, 2, 1, 1, 8)]

Period length 6 — the block in parentheses repeats forever.

Representations

In words: twenty-one
Ordinal: 21st
Roman numeral: XXI
Binary: 10101
Octal: 25
Hexadecimal: 0x15
Base64: FQ==
One's complement: 234 (8-bit)
Scientific notation: 2.1 × 10¹

In other bases

ternary (3) 210

quaternary (4) 111

quinary (5) 41

senary (6) 33

septenary (7) 30

nonary (9) 23

undecimal (11) 1a

duodecimal (12) 19

tridecimal (13) 18

tetradecimal (14) 17

pentadecimal (15) 16

Palindromic in base 2, base 4

As an angle

21°

21° ≈ 0.367 rad

Compass bearing: NNE (north-northeast)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒌋𒁹
Egyptian hieroglyphic: 𓎆𓎆𓏺
Greek (Milesian): καʹ
Mayan (base 20): 𝋡·𝋡
Chinese: 二十一
Chinese (financial): 貳拾壹

In other modern scripts

Eastern Arabic ٢١ Devanagari २१ Bengali ২১ Tamil ௨௧ Thai ๒๑ Tibetan ༢༡ Khmer ២១ Lao ໒໑ Burmese ၂၁

Digit at this position in famous constants

π — Pi (π): Digit 21 = 6
e — Euler's number (e): Digit 21 = 6
φ — Golden ratio (φ): Digit 21 = 0
√2 — Pythagoras's (√2): Digit 21 = 0
ln 2 — Natural log of 2: Digit 21 = 1
γ — Euler-Mascheroni (γ): Digit 21 = 0

Also seen as

ASCII character

As an ASCII codepoint, 21 is control character (0x15). ASCII control character.

Network port

TCP/UDP port 21 is the well-known port for FTP — File Transfer Protocol — control channel.

Hex color

#000015

RGB(0, 0, 21)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.0.21.

Address: 0.0.0.21
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.0.21

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

Musical pitch

Heard as a frequency, 21 Hz is closest to:

Concert pitch (A4 = 440 Hz): E0 (20.6 Hz, +33¢)
Scientific pitch (C4 = 256 Hz): F0 (21.4 Hz, -29¢)
Baroque pitch (A4 = 415 Hz): F0 (20.6 Hz, +34¢)

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

As a MIDI note number, 21 is A0 (27.5 Hz at concert pitch) — the lowest note on a standard 88-key piano. (very low — many laptop and phone speakers can't reproduce it)

Atomic number

On the periodic table, atomic number 21 is Scandium (Sc) — period 4.

Scandium on Wikipedia ↗