Number

10

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

10 (ten) is an even 2-digit number. It is a composite number with 4 divisors, and factors as 2 × 5. It is the fourth triangular number and a power of ten (10¹). Written other ways, in Roman numerals it is X and in binary, 1010.

Centered Triangular Cube-Free Decagonal Deficient Number Evil Number Flippable Happy Number Harshad / Niven Highly Abundant Pernicious Number Perrin Number Power of Ten Preferred Number Recamán's Sequence Semiprime Squarefree Tetrahedral Triangular Year

Interestingness

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Historical context — 10 AD

Calendar year

AD 10 (X) 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 — 10 BC

Calendar year

Year 10 BC was either a common year starting on Tuesday, Wednesday or Thursday or a leap year starting on Tuesday or Wednesday of the Julian calendar and a common 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, 10
Ended on: Friday
December 31, 10
Friday the 13ths: 1
One Friday the 13th this year.
Decade: 10s
10–19
Century: 1st century
1–100
Millennium: 1st millennium
1–1000
Years ago: 2,016
2016 years before 2026.

In other calendars

Hebrew: 3770 / 3771 AM
Rosh Hashanah falls in September/October.
Chinese: Year of the zodiac:Metal zodiac:Horse
Sexagenary cycle position 7 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 553 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: 2 / 3 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): -68 / -69 Saka
Indian national calendar; year starts in March.

Cultural significance

Western significant

The basis of the decimal system; "a perfect ten" in scoring.

Ten fingers gave humans their counting base.

Jewish/Christian sacred

The Ten Commandments.

Decalogue given to Moses on Mount Sinai.

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

Properties

Parity: Even
Digit count: 2
Digit sum: 1
Digit product: 0
Digital root: 1
Palindrome: No
Bit width: 4 bits
Reversed: 1
Flips to (rotate 180°): 1
Recamán's sequence: a(12) = 10
Square (n²): 100
Cube (n³): 1,000
Divisor count: 4
σ(n) — sum of divisors: 18
φ(n) — Euler's totient: 4
Sum of prime factors: 7

Primality

Prime factorization: 2 × 5

Nearest primes: 7 (−3) · 11 (+1)

Divisors & multiples

All divisors (4)

1 · 2 · 5 (half) · 10

Aliquot sum (sum of proper divisors): 8

Factor pairs (a × b = 10)

1 × 10

2 × 5

First multiples

10 · 20 (double) · 30 · 40 · 50 · 60 · 70 · 80 · 90 · 100

Sums & aliquot sequence

As a sum of two squares: 1² + 3²

As consecutive integers: 1 + 2 + 3 + 4

Aliquot sequence: 10 → 8 → 7 → 1 → 0 — terminates at zero

Continued fraction of √n

√10 = [3; (6)]

Period length 1 — the block in parentheses repeats forever.

Representations

In words: ten
Ordinal: 10th
Roman numeral: X
Binary: 1010
Octal: 12
Hexadecimal: 0xA
Base64: Cg==
One's complement: 245 (8-bit)
Scientific notation: 1 × 10¹

In other bases

ternary (3) 101

quaternary (4) 22

quinary (5) 20

senary (6) 14

septenary (7) 13

nonary (9) 11

undecimal (11) a

duodecimal (12) a

tridecimal (13) a

tetradecimal (14) a

pentadecimal (15) a

Palindromic in base 3

As an angle

10°

10° ≈ 0.175 rad

Compass bearing: N (north)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋
Egyptian hieroglyphic: 𓎆
Greek (Milesian): ιʹ
Mayan (base 20): 𝋪
Chinese: 一十
Chinese (financial): 壹拾

In other modern scripts

Eastern Arabic ١٠ Devanagari १० Bengali ১০ Tamil ௧௦ Thai ๑๐ Tibetan ༡༠ Khmer ១០ Lao ໑໐ Burmese ၁၀

Digit at this position in famous constants

π — Pi (π): Digit 10 = 3
e — Euler's number (e): Digit 10 = 8
φ — Golden ratio (φ): Digit 10 = 8
√2 — Pythagoras's (√2): Digit 10 = 2
ln 2 — Natural log of 2: Digit 10 = 0
γ — Euler-Mascheroni (γ): Digit 10 = 4

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 10, here are decompositions:

3 + 7 = 10
5 + 5 = 10

ASCII character

As an ASCII codepoint, 10 is LF (line feed). ASCII control character.

Hex color

#00000A

RGB(0, 0, 10)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.0.10.

Address: 0.0.0.10
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.0.10

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

US numbered highway

Matches numbered highway designation:

I-10 — Santa Monica, CA to Jacksonville, FL — the southernmost coast-to-coast Interstate.

Interstate 10 on Wikipedia ↗

Musical pitch

As a MIDI note number, 10 is A♯-1 (14.6 Hz at concert pitch). (below the ~20 Hz floor of human hearing — likely inaudible)

Atomic number

On the periodic table, atomic number 10 is Neon (Ne) — period 2.

Neon on Wikipedia ↗