Number

60

60 — Sexagesimal Base

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

Sixty is the smallest number divisible by every integer from 1 to 6. The Babylonian sexagesimal (base-60) system is why we still have 60 seconds in a minute and 60 minutes in an hour.

Sources https://en.wikipedia.org/wiki/60_(number)

Abundant Number Arithmetic Number Cube-Free Curated Evil Number Flippable Harshad / Niven Highly Abundant Highly Composite Number Practical Number Recamán's Sequence Refactorable Number Semiperfect Number

Interestingness

★ ★ ★ ★ ★

10 notable facts · grade A

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Historical context — 60 AD

Calendar year

AD 60 (LX) was a leap year starting on Tuesday of the Julian calendar.

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

Notable events — 60 BC

Undated Caesar, Pompey, and Crassus form the First Triumvirate.

Events compiled from Wikipedia ↗ · Licensed CC BY-SA 4.0

Year facts

Year type: Leap year
Divisible by 4 and not by 100; February has 29 days.
Days in year: 366
ISO weeks: 53
Long year: contains 53 ISO weeks.
Started on: Thursday
January 1, 60
Ended on: Friday
December 31, 60
Friday the 13ths: 2
2 Friday the 13ths this year.
Decade: 60s
60–69
Century: 1st century
1–100
Millennium: 1st millennium
1–1000
Years ago: 1,966
1966 years before 2026.

In other calendars

Hebrew: 3820 / 3821 AM
Rosh Hashanah falls in September/October.
Chinese: Year of the zodiac:Metal zodiac:Monkey
Sexagenary cycle position 57 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 603 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: 52 / 53 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): -18 / -19 Saka
Indian national calendar; year starts in March.

Cultural significance

Babylonian significant

Base of the sexagesimal system — why we have 60 seconds, 60 minutes, and 360°.

Highly composite, with many divisors.

Chinese significant

Length of the traditional Chinese cycle (combining 10 heavenly stems and 12 earthly branches).

60-year cycle in the Chinese calendar; one's 60th birthday is a major celebration.

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

Properties

Parity: Even
Digit count: 2
Digit sum: 6
Digit product: 0
Digital root: 6
Palindrome: No
Bit width: 6 bits
Reversed: 6
Flips to (rotate 180°): 9
Recamán's sequence: a(196) = 60
Square (n²): 3,600
Cube (n³): 216,000
Divisor count: 12
σ(n) — sum of divisors: 168
φ(n) — Euler's totient: 16
Sum of prime factors: 12

Primality

Prime factorization: 2 ² × 3 × 5

Nearest primes: 59 (−1) · 61 (+1)

Divisors & multiples

All divisors (12)

1 · 2 · 3 · 4 · 5 · 6 · 10 · 12 · 15 · 20 · 30 (half) · 60

Aliquot sum (sum of proper divisors): 108

Factor pairs (a × b = 60)

1 × 60

2 × 30

3 × 20

4 × 15

5 × 12

6 × 10

First multiples

60 · 120 (double) · 180 · 240 · 300 · 360 · 420 · 480 · 540 · 600

Sums & aliquot sequence

As consecutive integers: 19 + 20 + 21 10 + 11 + 12 + 13 + 14 4 + 5 + … + 11

Aliquot sequence: 60 → 108 → 172 → 136 → 134 → 70 → 74 → 40 → 50 → 43 → 1 → 0 — terminates at zero

Continued fraction of √n

√60 = [7; (1, 2, 1, 14)]

Period length 4 — the block in parentheses repeats forever.

Representations

In words: sixty
Ordinal: 60th
Roman numeral: LX
Binary: 111100
Octal: 74
Hexadecimal: 0x3C
Base64: PA==
One's complement: 195 (8-bit)
Scientific notation: 6 × 10¹
As a duration: 60 s = 1 minute

In other bases

ternary (3) 2020

quaternary (4) 330

quinary (5) 220

senary (6) 140

septenary (7) 114

nonary (9) 66

undecimal (11) 55

duodecimal (12) 50

tridecimal (13) 48

tetradecimal (14) 44

pentadecimal (15) 40

As an angle

60°

60° ≈ 1.047 rad

Compass bearing: ENE (east-northeast)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹 ·
Egyptian hieroglyphic: 𓎆𓎆𓎆𓎆𓎆𓎆
Greek (Milesian): ξʹ
Mayan (base 20): 𝋣·𝋠
Chinese: 六十
Chinese (financial): 陸拾

In other modern scripts

Eastern Arabic ٦٠ Devanagari ६० Bengali ৬০ Tamil ௬௦ Thai ๖๐ Tibetan ༦༠ Khmer ៦០ Lao ໖໐ Burmese ၆၀

Digit at this position in famous constants

π — Pi (π): Digit 60 = 4
e — Euler's number (e): Digit 60 = 6
φ — Golden ratio (φ): Digit 60 = 4
√2 — Pythagoras's (√2): Digit 60 = 7
ln 2 — Natural log of 2: Digit 60 = 8
γ — Euler-Mascheroni (γ): Digit 60 = 6

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 60, here are decompositions:

7 + 53 = 60
13 + 47 = 60
17 + 43 = 60
19 + 41 = 60
23 + 37 = 60
29 + 31 = 60

ASCII character

As an ASCII codepoint, 60 is <. Printable ASCII character <.

Hex color

#00003C

RGB(0, 0, 60)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.0.60.

Address: 0.0.0.60
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.0.60

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

US numbered highway

Matches numbered highway designation:

US 60 — Virginia Beach, VA to Brenda, AZ.

US 60 on Wikipedia ↗

Geographic coordinate

As a geographic coordinate in degrees, this matches:

60th parallel (latitude) — The southern boundary of Yukon, Northwest Territories, and Nunavut; passes through Stockholm and Saint Petersburg.

World map (equirectangular projection) — Latitude 60° — 60th parallel

Musical pitch

Heard as a frequency, 60 Hz is closest to:

Concert pitch (A4 = 440 Hz): B1 (61.7 Hz, -49¢ — about midway to A♯1)
Scientific pitch (C4 = 256 Hz): B1 (60.4 Hz, -12¢)
Baroque pitch (A4 = 415 Hz): C2 (61.7 Hz, -48¢ — about midway to B1)

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

Roughly B♭1 — and the frequency of North American mains-electricity hum.

As a MIDI note number, 60 is C4 (261.6 Hz at concert pitch) — middle C.

Atomic number

On the periodic table, atomic number 60 is Neodymium (Nd) — period 6.

Neodymium on Wikipedia ↗

Angle

60° is π/3 radians — the interior angle of an equilateral triangle.

Time & calendar

60 is the number of seconds in a minute and minutes in an hour — the base of the sexagesimal timekeeping the Babylonians handed down.

Units of time — Wikipedia ↗