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Number

108

108 — The most auspicious number

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

108 is sacred across Hinduism, Buddhism, Jainism and Sikhism — arguably the most broadly revered number on earth. A mala, the prayer-bead string used for recitation, carries 108 beads. Major deities are honoured with 108 names. Buddhist tradition enumerates 108 kleshas, the defilements that bind a person to suffering.

It is a number you can hear as much as count. On New Year's Eve, Japanese temples toll the bell 108 times — Joya no Kane — one strike for each worldly desire to be let go before the year turns. Yoga practitioners mark the solstices with 108 sun salutations, and Ayurvedic medicine maps 108 marma points on the body.

Why 108? The explanations multiply, which is itself part of the appeal: 54 letters of the Sanskrit alphabet doubled for Shiva and Shakti; the astronomical near-coincidences that the Sun sits roughly 108 solar diameters from Earth and the Moon roughly 108 lunar diameters. Mathematically it is tidy in its own right — 108 = 1¹ × 2² × 3³ — and abundant. A regulation baseball, meanwhile, has exactly 108 double stitches, a fact with no spiritual content whatsoever, which is somehow the most 108 thing about 108.

Sources https://en.wikipedia.org/wiki/108_(number) · https://en.wikipedia.org/wiki/Japanese_New_Year
Abundant Number Achilles Number Curated Evil Number Flippable Gapful Number Harshad / Niven Highly Abundant Powerful Number Practical Number Recamán's Sequence Refactorable Number Self Number Semiperfect Number Tetranacci Number

Interestingness

12 notable facts · grade A
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Historical context — 108 AD

Calendar year

Year 108 (CVIII) was a leap year starting on Saturday of the Julian calendar.

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

Historical context — 108 BC

Calendar year

108 BC was a year of the pre-Julian Roman 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
Sunday
January 1, 108
Ended on
Monday
December 31, 108
Friday the 13ths
3
3 Friday the 13ths this year.
Decade
100s
100–109
Century
2nd century
101–200
Millennium
1st millennium
1–1000
Years ago
1,918
1918 years before 2026.

In other calendars

Hebrew
3868 / 3869 AM
Rosh Hashanah falls in September/October.
Chinese
Year of the zodiac:Earth zodiac:Monkey
Sexagenary cycle position 45 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era
651 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian
100 / 101 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka)
30 / 29 Saka
Indian national calendar; year starts in March.

Cultural significance

Hindu sacred

The number of beads on a mala (prayer rosary); 108 names of major deities.

Considered the most auspicious number in Hindu tradition.

Wikipedia ↗

Buddhist sacred

108 mortal desires / defilements (kleshas); 108 mala beads; Japanese New Year bell rung 108 times.

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

Properties

Parity
Even
Digit count
3
Digit sum
9
Digit product
0
Digital root
9
Palindrome
No
Bit width
7 bits
Reversed
801
Flips to (rotate 180°)
801
Recamán's sequence
a(371) = 108
Square (n²)
11,664
Cube (n³)
1,259,712
Divisor count
12
σ(n) — sum of divisors
280
φ(n) — Euler's totient
36
Sum of prime factors
13

Primality

Prime factorization: 2 2 × 3 3

Nearest primes: 107 (−1) · 109 (+1)

Divisors & multiples

All divisors (12)
1 · 2 · 3 · 4 · 6 · 9 · 12 · 18 · 27 · 36 · 54 (half) · 108
Aliquot sum (sum of proper divisors): 172
Factor pairs (a × b = 108)
1 × 108
2 × 54
3 × 36
4 × 27
6 × 18
9 × 12
First multiples
108 · 216 (double) · 324 · 432 · 540 · 648 · 756 · 864 · 972 · 1,080

Sums & aliquot sequence

As consecutive integers: 35 + 36 + 37 10 + 11 + … + 17 8 + 9 + … + 16
Aliquot sequence: 108 172 136 134 70 74 40 50 43 1 0 — terminates at zero

Continued fraction of √n

√108 = [10; (2, 1, 1, 4, 1, 1, 2, 20)]

Period length 8 — the block in parentheses repeats forever.

Representations

In words
one hundred eight
Ordinal
108th
Roman numeral
CVIII
Binary
1101100
Octal
154
Hexadecimal
0x6C
Base64
bA==
One's complement
147 (8-bit)
Scientific notation
1.08 × 10²
As a duration
108 s = 1 minute, 48 seconds
In other bases
ternary (3) 11000
quaternary (4) 1230
quinary (5) 413
senary (6) 300
septenary (7) 213
nonary (9) 130
undecimal (11) 99
duodecimal (12) 90
tridecimal (13) 84
tetradecimal (14) 7a
pentadecimal (15) 73

As an angle

108°
108° ≈ 1.885 rad
Compass bearing: ESE (east-southeast)

Historical numeral systems

Babylonian (base 60)
𒁹 𒌋𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic
𓍢𓏺𓏺𓏺𓏺𓏺𓏺𓏺𓏺
Greek (Milesian)
ρηʹ
Mayan (base 20)
𝋥·𝋨
Chinese
一百零八
Chinese (financial)
壹佰零捌
In other modern scripts
Eastern Arabic ١٠٨ Devanagari १०८ Bengali ১০৮ Tamil ௧௦௮ Thai ๑๐๘ Tibetan ༡༠༨ Khmer ១០៨ Lao ໑໐໘ Burmese ၁၀၈

Digit at this position in famous constants

π — Pi (π)
Digit 108 = 8
e — Euler's number (e)
Digit 108 = 9
φ — Golden ratio (φ)
Digit 108 = 8
√2 — Pythagoras's (√2)
Digit 108 = 4
ln 2 — Natural log of 2
Digit 108 = 8
γ — Euler-Mascheroni (γ)
Digit 108 = 4

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 108, here are decompositions:

  • 5 + 103 = 108
  • 7 + 101 = 108
  • 11 + 97 = 108
  • 19 + 89 = 108
  • 29 + 79 = 108
  • 37 + 71 = 108
  • 41 + 67 = 108
  • 47 + 61 = 108

Showing the first eight; more decompositions exist.

ASCII character

As an ASCII codepoint, 108 is l. Printable ASCII character l.

Hex color
#00006C
RGB(0, 0, 108)
IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.0.108.

Address
0.0.0.108
Class
reserved
IPv4-mapped IPv6
::ffff:0.0.0.108

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

Musical pitch

Heard as a frequency, 108 Hz is closest to:

  • Concert pitch (A4 = 440 Hz): A2 (110 Hz, -32¢)
  • Scientific pitch (C4 = 256 Hz): A2 (107.6 Hz, +6¢)
  • Baroque pitch (A4 = 415 Hz): A♯2 (109.9 Hz, -30¢)
(very low — many laptop and phone speakers can't reproduce it)

As a MIDI note number, 108 is C8 (4186 Hz at concert pitch) — the highest note on a standard 88-key piano.

Atomic number

On the periodic table, atomic number 108 is Hassium (Hs) — period 7.

Related reading

  • Babylonian numerals — The base-60 cuneiform system that gave us 60 minutes, 60 seconds, and 360°.