72
72 is a composite number, even, a calendar year.
Few numbers lead a double life as cleanly as 72. To a financier it is a mental shortcut: the Rule of 72 says that dividing 72 by an annual growth rate gives the years needed to double — money at 6% doubles in about twelve years, at 8% in about nine. It works because 72 sits close to 100 × ln 2 (≈ 69.3) and happens to divide neatly by 2, 3, 4, 6, 8 and 9, so the arithmetic stays easy in the head.
To a Kabbalist, 72 is the hidden name of God. Exodus 14:19–21 — the parting of the sea — is three consecutive verses of exactly 72 letters each; read in a boustrophedon weave they yield the Shem HaMephorash, the 72 three-letter names. The number recurs across religion with the same air of near-completeness: 72 disciples sent out in Luke, 72 nations traditionally descended from Noah, 72 languages scattered at Babel, the 72 scholars said to have translated the Septuagint.
The mathematics is quietly obliging too. 72 = 2³ × 3², it is the sum of four consecutive primes (13 + 17 + 19 + 23), and 72° is the central angle of a regular pentagon — the exact turn that carries one point of a five-pointed star to the next. A doubling rule, a divine name, and the geometry of a star, all filed under the same integer.
Interestingness
Historical context — 72 AD
Calendar year
AD 72 (LXXII) was a leap year starting on Wednesday of the Julian calendar.
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Historical context — 72 BC
Calendar year
Year 72 BC was a year of the pre-Julian Roman calendar.
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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
-
Friday
January 1, 72
- Ended on
-
Saturday
December 31, 72
- Friday the 13ths
-
1
One Friday the 13th this year.
- Decade
-
70s
70–79
- Century
-
1st century
1–100
- Millennium
-
1st millennium
1–1000
- Years ago
-
1,954
1954 years before 2026.
In other calendars
- Hebrew
-
3832 / 3833 AM
Rosh Hashanah falls in September/October.
- Chinese
-
Year of the zodiac:Water zodiac:Monkey
Sexagenary cycle position 9 of 60. Lunar new year falls in late January / mid-February.
- Buddhist Era
-
615 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
- Ethiopian
-
64 / 65 ET
Year boundary at Enkutatash (September 11/12).
- Indian National (Saka)
-
-6 / -7 Saka
Indian national calendar; year starts in March.
Cultural significance
The 72 names of God in Kabbalah.
Derived from a permutation of three verses in Exodus 14.
Sourced from Wikipedia (Numerology, Chinese numerology, Gematria, and per-culture articles).
Properties
Primality
Prime factorization: 2 3 × 3 2
Divisors & multiples
Sums & aliquot sequence
Continued fraction of √n
√72 = [8; (2, 16)]
Period length 2 — the block in parentheses repeats forever.
Representations
- In words
- seventy-two
- Ordinal
- 72nd
- Roman numeral
- LXXII
- Binary
- 1001000
- Octal
- 110
- Hexadecimal
- 0x48
- Base64
- SA==
- One's complement
- 183 (8-bit)
- Scientific notation
- 7.2 × 10¹
- As a duration
- 72 s = 1 minute, 12 seconds
As an angle
Historical numeral systems
- Babylonian (base 60)
- 𒁹 𒌋𒁹𒁹
- Egyptian hieroglyphic
- 𓎆𓎆𓎆𓎆𓎆𓎆𓎆𓏺𓏺
- Greek (Milesian)
- οβʹ
- Mayan (base 20)
- 𝋣·𝋬
- Chinese
- 七十二
- Chinese (financial)
- 柒拾貳
Digit at this position in famous constants
- π — Pi (π)
- Digit 72 = 0
- e — Euler's number (e)
- Digit 72 = 3
- φ — Golden ratio (φ)
- Digit 72 = 6
- √2 — Pythagoras's (√2)
- Digit 72 = 7
- ln 2 — Natural log of 2
- Digit 72 = 2
- γ — Euler-Mascheroni (γ)
- Digit 72 = 2
Also seen as
Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 72, here are decompositions:
- 5 + 67 = 72
- 11 + 61 = 72
- 13 + 59 = 72
- 19 + 53 = 72
- 29 + 43 = 72
- 31 + 41 = 72
As an ASCII codepoint, 72 is H. Printable ASCII character H.
As an unsigned 32-bit integer, this is the IPv4 address 0.0.0.72.
- Address
- 0.0.0.72
- Class
- reserved
- IPv4-mapped IPv6
- ::ffff:0.0.0.72
Unspecified address (0.0.0.0/8) — "this network" placeholder.
Matches numbered highway designation:
- I-72 — Hannibal, MO to Champaign, IL.
Heard as a frequency, 72 Hz is closest to:
- Concert pitch (A4 = 440 Hz): D2 (73.4 Hz, -34¢)
- Scientific pitch (C4 = 256 Hz): D2 (71.8 Hz, +4¢)
- Baroque pitch (A4 = 415 Hz): D♯2 (73.4 Hz, -32¢)
As a MIDI note number, 72 is C5 (523.3 Hz at concert pitch).
On the periodic table, atomic number 72 is Hafnium (Hf) — period 6.
Related reading
- Babylonian numerals — The base-60 cuneiform system that gave us 60 minutes, 60 seconds, and 360°.