Number

117

117 is a composite number, odd, a calendar year.

117 (one hundred seventeen) is an odd 3-digit number. It is a composite number with 6 divisors, and factors as 3² × 13. Written other ways, in Roman numerals it is CXVII and in binary, 1110101.

Cube-Free Deficient Number Harshad / Niven Moran Number Odious Number Pentagonal Pernicious Number Recamán's Sequence Year

Interestingness

★ ★ ★ ☆ ☆

5 notable facts · grade C

105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129

less more

Notable events — 117 AD

Aug 11 Hadrian succeeds Trajan, marking the empire's greatest territorial extent.

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

Historical context — 117 BC

Calendar year

Year 117 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: Friday
January 1, 117
Ended on: Friday
December 31, 117
Friday the 13ths: 1
One Friday the 13th this year.
Decade: 110s
110–119
Century: 2nd century
101–200
Millennium: 1st millennium
1–1000
Years ago: 1,909
1909 years before 2026.

In other calendars

Hebrew: 3877 / 3878 AM
Rosh Hashanah falls in September/October.
Chinese: Year of the zodiac:Fire zodiac:Snake
Sexagenary cycle position 54 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 660 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: 109 / 110 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 39 / 38 Saka
Indian national calendar; year starts in March.

Properties

Parity: Odd
Digit count: 3
Digit sum: 9
Digit product: 7
Digital root: 9
Palindrome: No
Bit width: 7 bits
Reversed: 711
Recamán's sequence: a(166) = 117
Square (n²): 13,689
Cube (n³): 1,601,613
Divisor count: 6
σ(n) — sum of divisors: 182
φ(n) — Euler's totient: 72
Sum of prime factors: 19

Primality

Prime factorization: 3 ² × 13

Nearest primes: 113 (−4) · 127 (+10)

Divisors & multiples

All divisors (6)

1 · 3 · 9 · 13 · 39 · 117

Aliquot sum (sum of proper divisors): 65

Factor pairs (a × b = 117)

1 × 117

3 × 39

9 × 13

First multiples

117 · 234 (double) · 351 · 468 · 585 · 702 · 819 · 936 · 1,053 · 1,170

Sums & aliquot sequence

As a sum of two squares: 6² + 9²

As consecutive integers: 58 + 59 38 + 39 + 40 17 + 18 + 19 + 20 + 21 + 22 9 + 10 + … + 17

Aliquot sequence: 117 → 65 → 19 → 1 → 0 — terminates at zero

Continued fraction of √n

√117 = [10; (1, 4, 2, 4, 1, 20)]

Period length 6 — the block in parentheses repeats forever.

Representations

In words: one hundred seventeen
Ordinal: 117th
Roman numeral: CXVII
Binary: 1110101
Octal: 165
Hexadecimal: 0x75
Base64: dQ==
One's complement: 138 (8-bit)
Scientific notation: 1.17 × 10²
As a duration: 117 s = 1 minute, 57 seconds

In other bases

ternary (3) 11100

quaternary (4) 1311

quinary (5) 432

senary (6) 313

septenary (7) 225

nonary (9) 140

undecimal (11) a7

duodecimal (12) 99

tridecimal (13) 90

tetradecimal (14) 85

pentadecimal (15) 7c

Palindromic in base 6

As an angle

117°

117° ≈ 2.042 rad

Compass bearing: ESE (east-southeast)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹 𒌋𒌋𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓍢𓎆𓏺𓏺𓏺𓏺𓏺𓏺𓏺
Greek (Milesian): ριζʹ
Mayan (base 20): 𝋥·𝋱
Chinese: 一百一十七
Chinese (financial): 壹佰壹拾柒

In other modern scripts

Eastern Arabic ١١٧ Devanagari ११७ Bengali ১১৭ Tamil ௧௧௭ Thai ๑๑๗ Tibetan ༡༡༧ Khmer ១១៧ Lao ໑໑໗ Burmese ၁၁၇

Digit at this position in famous constants

π — Pi (π): Digit 117 = 0
e — Euler's number (e): Digit 117 = 5
φ — Golden ratio (φ): Digit 117 = 9
√2 — Pythagoras's (√2): Digit 117 = 9
ln 2 — Natural log of 2: Digit 117 = 8
γ — Euler-Mascheroni (γ): Digit 117 = 8

Also seen as

ASCII character

As an ASCII codepoint, 117 is u. Printable ASCII character u.

Hex color

#000075

RGB(0, 0, 117)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.0.117.

Address: 0.0.0.117
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.0.117

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

Musical pitch

Heard as a frequency, 117 Hz is closest to:

Concert pitch (A4 = 440 Hz): A♯2 (116.5 Hz, +7¢)
Scientific pitch (C4 = 256 Hz): A♯2 (114 Hz, +44¢)
Baroque pitch (A4 = 415 Hz): B2 (116.5 Hz, +8¢)

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

As a MIDI note number, 117 is A8 (7040 Hz at concert pitch).

Atomic number

On the periodic table, atomic number 117 is Tennessine (Ts) — period 7.

Tennessine on Wikipedia ↗