Number

36

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

36 (thirty-six) is an even 2-digit number. It is a composite number with 9 divisors, and factors as 2² × 3². Its proper divisors sum to 55, more than the number itself, making it an abundant number. It is the eighth triangular number and a perfect square (6²). Written other ways, in Roman numerals it is XXXVI and in binary, 100100.

Abundant Number Cube-Free Evil Number Harshad / Niven Highly Abundant Highly Composite Number Lucky Number Perfect Square Pernicious Number Powerful Number Practical Number Preferred Number Recamán's Sequence Refactorable Number Semiperfect Number Triangular Year Zuckerman Number

Interestingness

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14 notable facts · grade A

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Historical context — 36 AD

Calendar year

AD 36 (XXXVI) was a leap year starting on Sunday of the Julian calendar.

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

Historical context — 36 BC

Calendar year

Year 36 BC was either a common year starting on Tuesday, Wednesday or Thursday or a leap year starting on Wednesday of the Julian calendar and a common year starting on Wednesday 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: Leap year
Divisible by 4 and not by 100; February has 29 days.
Days in year: 366
ISO weeks: 52
Started on: Tuesday
January 1, 36
Ended on: Wednesday
December 31, 36
Friday the 13ths: 1
One Friday the 13th this year.
Decade: 30s
30–39
Century: 1st century
1–100
Millennium: 1st millennium
1–1000
Years ago: 1,990
1990 years before 2026.

In other calendars

Hebrew: 3796 / 3797 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: 579 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: 28 / 29 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): -42 / -43 Saka
Indian national calendar; year starts in March.

Cultural significance

Jewish sacred

The Lamed-Vavniks — 36 hidden righteous people on whom the world depends.

Talmudic tradition holds that in every generation 36 righteous souls ("tzadikim") secretly sustain the world.

Wikipedia ↗

Jewish lucky

Double chai — twice 18 ("life"); a common doubly-auspicious gift.

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

Properties

Parity: Even
Digit count: 2
Digit sum: 9
Digit product: 18
Digital root: 9
Palindrome: No
Bit width: 6 bits
Reversed: 63
Recamán's sequence: a(44) = 36
Square (n²): 1,296
Cube (n³): 46,656
Square root (√n): 6
Divisor count: 9
σ(n) — sum of divisors: 91
φ(n) — Euler's totient: 12
Sum of prime factors: 10

Primality

Prime factorization: 2 ² × 3 ²

Nearest primes: 31 (−5) · 37 (+1)

Divisors & multiples

All divisors (9)

1 · 2 · 3 · 4 · 6 · 9 · 12 · 18 (half) · 36

Aliquot sum (sum of proper divisors): 55

Factor pairs (a × b = 36)

1 × 36

2 × 18

3 × 12

4 × 9

6 × 6

First multiples

36 · 72 (double) · 108 · 144 · 180 · 216 · 252 · 288 · 324 · 360

Sums & aliquot sequence

As a sum of two squares: 0² + 6²

As consecutive integers: 11 + 12 + 13 1 + 2 + … + 8

Aliquot sequence: 36 → 55 → 17 → 1 → 0 — terminates at zero

Representations

In words: thirty-six
Ordinal: 36th
Roman numeral: XXXVI
Binary: 100100
Octal: 44
Hexadecimal: 0x24
Base64: JA==
One's complement: 219 (8-bit)
Scientific notation: 3.6 × 10¹

In other bases

ternary (3) 1100

quaternary (4) 210

quinary (5) 121

senary (6) 100

septenary (7) 51

nonary (9) 40

undecimal (11) 33

duodecimal (12) 30

tridecimal (13) 2a

tetradecimal (14) 28

pentadecimal (15) 26

Palindromic in base 5

As an angle

36°

36° ≈ 0.628 rad

Compass bearing: NE (northeast)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓎆𓎆𓎆𓏺𓏺𓏺𓏺𓏺𓏺
Greek (Milesian): λϛʹ
Mayan (base 20): 𝋡·𝋰
Chinese: 三十六
Chinese (financial): 參拾陸

In other modern scripts

Eastern Arabic ٣٦ Devanagari ३६ Bengali ৩৬ Tamil ௩௬ Thai ๓๖ Tibetan ༣༦ Khmer ៣៦ Lao ໓໖ Burmese ၃၆

Digit at this position in famous constants

π — Pi (π): Digit 36 = 8
e — Euler's number (e): Digit 36 = 9
φ — Golden ratio (φ): Digit 36 = 1
√2 — Pythagoras's (√2): Digit 36 = 7
ln 2 — Natural log of 2: Digit 36 = 6
γ — Euler-Mascheroni (γ): Digit 36 = 3

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 36, here are decompositions:

5 + 31 = 36
7 + 29 = 36
13 + 23 = 36
17 + 19 = 36

ASCII character

As an ASCII codepoint, 36 is $. Printable ASCII character $.

Hex color

#000024

RGB(0, 0, 36)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.0.36.

Address: 0.0.0.36
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.0.36

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

Musical pitch

Heard as a frequency, 36 Hz is closest to:

Concert pitch (A4 = 440 Hz): D1 (36.7 Hz, -34¢)
Scientific pitch (C4 = 256 Hz): D1 (35.9 Hz, +4¢)
Baroque pitch (A4 = 415 Hz): D♯1 (36.7 Hz, -32¢)

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

As a MIDI note number, 36 is C2 (65.4 Hz at concert pitch). (very low — many laptop and phone speakers can't reproduce it)

Atomic number

On the periodic table, atomic number 36 is Krypton (Kr) — period 4.

Krypton on Wikipedia ↗