Number

138

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

138 (one hundred thirty-eight) is an even 3-digit number. It is a composite number with 8 divisors, and factors as 2 × 3 × 23. Its proper divisors sum to 150, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is CXXXVIII and in binary, 10001010.

Abundant Number Arithmetic Number Ascending Digits Cube-Free Odious Number Pernicious Number Recamán's Sequence Semiperfect Number Sphenic Number Squarefree Year

Interestingness

★ ★ ★ ★ ☆

7 notable facts · grade B

126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150

less more

Historical context — 138 AD

Calendar year

Year 138 (CXXXVIII) was a common year starting on Tuesday of the Julian calendar.

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

Historical context — 138 BC

Calendar year

Year 138 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: Common year
Standard 365-day year; not divisible by 4 (or divisible by 100 but not 400).
Days in year: 365
ISO weeks: 52
Started on: Wednesday
January 1, 138
Ended on: Wednesday
December 31, 138
Friday the 13ths: 1
One Friday the 13th this year.
Decade: 130s
130–139
Century: 2nd century
101–200
Millennium: 1st millennium
1–1000
Years ago: 1,888
1888 years before 2026.

In other calendars

Hebrew: 3898 / 3899 AM
Rosh Hashanah falls in September/October.
Chinese: Year of the zodiac:Earth zodiac:Tiger
Sexagenary cycle position 15 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 681 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: 130 / 131 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 60 / 59 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 3
Digit sum: 12
Digit product: 24
Digital root: 3
Palindrome: No
Bit width: 8 bits
Reversed: 831
Recamán's sequence: a(120) = 138
Square (n²): 19,044
Cube (n³): 2,628,072
Divisor count: 8
σ(n) — sum of divisors: 288
φ(n) — Euler's totient: 44
Sum of prime factors: 28

Primality

Prime factorization: 2 × 3 × 23

Nearest primes: 137 (−1) · 139 (+1)

Divisors & multiples

All divisors (8)

1 · 2 · 3 · 6 · 23 · 46 · 69 (half) · 138

Aliquot sum (sum of proper divisors): 150

Factor pairs (a × b = 138)

1 × 138

2 × 69

3 × 46

6 × 23

First multiples

138 · 276 (double) · 414 · 552 · 690 · 828 · 966 · 1,104 · 1,242 · 1,380

Sums & aliquot sequence

As consecutive integers: 45 + 46 + 47 33 + 34 + 35 + 36 6 + 7 + … + 17

Aliquot sequence: 138 → 150 → 222 → 234 → 312 → 528 → 960 → 2,088 → 3,762 → 5,598 → 6,570 → 10,746 → 13,254 → 13,830 → 19,434 → 20,886 → 21,606 — unresolved within range

Continued fraction of √n

√138 = [11; (1, 2, 1, 22)]

Period length 4 — the block in parentheses repeats forever.

Representations

In words: one hundred thirty-eight
Ordinal: 138th
Roman numeral: CXXXVIII
Binary: 10001010
Octal: 212
Hexadecimal: 0x8A
Base64: ig==
One's complement: 117 (8-bit)
Scientific notation: 1.38 × 10²
As a duration: 138 s = 2 minutes, 18 seconds

In other bases

ternary (3) 12010

quaternary (4) 2022

quinary (5) 1023

senary (6) 350

septenary (7) 255

nonary (9) 163

undecimal (11) 116

duodecimal (12) b6

tridecimal (13) a8

tetradecimal (14) 9c

pentadecimal (15) 93

Palindromic in base 8

As an angle

138°

138° ≈ 2.409 rad

Compass bearing: SE (southeast)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹 𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓍢𓎆𓎆𓎆𓏺𓏺𓏺𓏺𓏺𓏺𓏺𓏺
Greek (Milesian): ρληʹ
Mayan (base 20): 𝋦·𝋲
Chinese: 一百三十八
Chinese (financial): 壹佰參拾捌

In other modern scripts

Eastern Arabic ١٣٨ Devanagari १३८ Bengali ১৩৮ Tamil ௧௩௮ Thai ๑๓๘ Tibetan ༡༣༨ Khmer ១៣៨ Lao ໑໓໘ Burmese ၁၃၈

Digit at this position in famous constants

π — Pi (π): Digit 138 = 3
e — Euler's number (e): Digit 138 = 7
φ — Golden ratio (φ): Digit 138 = 3
√2 — Pythagoras's (√2): Digit 138 = 1
ln 2 — Natural log of 2: Digit 138 = 5
γ — Euler-Mascheroni (γ): Digit 138 = 3

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 138, here are decompositions:

7 + 131 = 138
11 + 127 = 138
29 + 109 = 138
31 + 107 = 138
37 + 101 = 138
41 + 97 = 138
59 + 79 = 138
67 + 71 = 138

Showing the first eight; more decompositions exist.

Unicode codepoint

Line Tabulation Set

U+008A

Control character (Cc)

UTF-8 encoding: C2 8A (2 bytes).

Lookup U+008A on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#00008A

RGB(0, 0, 138)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.0.138.

Address: 0.0.0.138
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.0.138

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

Musical pitch

Heard as a frequency, 138 Hz is closest to:

Concert pitch (A4 = 440 Hz): C♯3 (138.6 Hz, -7¢)
Scientific pitch (C4 = 256 Hz): C♯3 (135.6 Hz, +30¢)
Baroque pitch (A4 = 415 Hz): D3 (138.5 Hz, -6¢)