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Number

84

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

Abundant Number Harshad / Niven Odious Number Pernicious Number Practical Number Recamán's Sequence Semiperfect Number Tetrahedral Year

Historical context — 84 AD

Calendar year

AD 84 (LXXXIV) was a leap year starting on Thursday of the Julian calendar.

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Historical context — 84 BC

Calendar year

Year 84 BC was a year of the pre-Julian Roman calendar.

Excerpt from Wikipedia (en) ↗ · Licensed CC BY-SA 4.0 · English fallback 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
Saturday
January 1, 84
Ended on
Sunday
December 31, 84
Friday the 13ths
1
One Friday the 13th this year.
Decade
80s
80–89
Century
1st century
1–100
Millennium
1st millennium
1–1000
Years ago
1,942
1942 years before 2026.

In other calendars

Hebrew
3844 / 3845 AM
Rosh Hashanah falls in September/October.
Chinese
Year of the zodiac:Wood zodiac:Monkey
Sexagenary cycle position 21 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era
627 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian
76 / 77 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka)
6 / 5 Saka
Indian national calendar; year starts in March.

Properties

Parity
Even
Digit count
2
Digit sum
12
Digit product
32
Digital root
3
Palindrome
No
Bit width
7 bits
Reversed
48
Recamán's sequence
a(51) = 84
Square (n²)
7,056
Cube (n³)
592,704
Divisor count
12
σ(n) — sum of divisors
224
φ(n) — Euler's totient
24
Sum of prime factors
14

Primality

Prime factorization: 2 2 × 3 × 7

Nearest primes: 83 (−1) · 89 (+5)

Divisors & multiples

All divisors (12)
1 · 2 · 3 · 4 · 6 · 7 · 12 · 14 · 21 · 28 · 42 (half) · 84
Aliquot sum (sum of proper divisors): 140
Factor pairs (a × b = 84)
1 × 84
2 × 42
3 × 28
4 × 21
6 × 14
7 × 12
First multiples
84 · 168 (double) · 252 · 336 · 420 · 504 · 588 · 672 · 756 · 840

Sums & aliquot sequence

As consecutive integers: 27 + 28 + 29 9 + 10 + … + 15 7 + 8 + … + 14
Aliquot sequence: 84 140 196 203 37 1 0 — terminates at zero

Representations

In words
eighty-four
Ordinal
84th
Roman numeral
LXXXIV
Binary
1010100
Octal
124
Hexadecimal
0x54
Base64
VA==
One's complement
171 (8-bit)
In other bases
ternary (3) 10010
quaternary (4) 1110
quinary (5) 314
senary (6) 220
septenary (7) 150
nonary (9) 103
undecimal (11) 77
duodecimal (12) 70
tridecimal (13) 66
tetradecimal (14) 60
pentadecimal (15) 59

Historical numeral systems

Babylonian (base 60)
𒁹 𒌋𒌋𒁹𒁹𒁹𒁹
Egyptian hieroglyphic
𓎆𓎆𓎆𓎆𓎆𓎆𓎆𓎆𓏺𓏺𓏺𓏺
Greek (Milesian)
πδʹ
Mayan (base 20)
𝋤·𝋤
Chinese
八十四
Chinese (financial)
捌拾肆
In other modern scripts
Eastern Arabic ٨٤ Devanagari ८४ Bengali ৮৪ Tamil ௮௪ Thai ๘๔ Tibetan ༨༤ Khmer ៨៤ Lao ໘໔ Burmese ၈၄

Digit at this position in famous constants

π — Pi (π)
Digit 84 = 2
e — Euler's number (e)
Digit 84 = 7
φ — Golden ratio (φ)
Digit 84 = 0
√2 — Pythagoras's (√2)
Digit 84 = 5
ln 2 — Natural log of 2
Digit 84 = 0
γ — Euler-Mascheroni (γ)
Digit 84 = 3

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 84, here are decompositions:

  • 5 + 79 = 84
  • 11 + 73 = 84
  • 13 + 71 = 84
  • 17 + 67 = 84
  • 23 + 61 = 84
  • 31 + 53 = 84
  • 37 + 47 = 84
  • 41 + 43 = 84

Showing the first eight; more decompositions exist.

ASCII character

As an ASCII codepoint, 84 is T. Printable ASCII character T.

Hex color
#000054
RGB(0, 0, 84)
IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.0.84.

Address
0.0.0.84
Class
reserved
IPv4-mapped IPv6
::ffff:0.0.0.84

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

US numbered highway

Matches numbered highway designation:

  • I-84 — Two segments: Portland, OR→Echo, UT and Scranton, PA→Sturbridge, MA.
Possible US bank routing number

This passes the ABA routing number checksum and matches the Federal Reserve numbering scheme.

Routing number
000000084
Federal Reserve
United States Government

Banks operate many routing numbers per state and division; an unmatched checksum-valid number can still be a real RTN at a smaller institution.