Number

113

113 is a prime, odd, a calendar year.

Arithmetic Number Chen Prime Cousin Prime Deficient Number Emirp Evil Number Prime Pythagorean Prime Recamán's Sequence Sexy Prime Sophie Germain Prime Squarefree Year

Historical context — 113 AD

Calendar year

Year 113 (CXIII) was a common year starting on Saturday of the Julian calendar.

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Historical context — 113 BC

Calendar year

Year 113 BC was a year of the pre-Julian Roman calendar.

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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: Sunday
January 1, 113
Ended on: Sunday
December 31, 113
Friday the 13ths: 2
2 Friday the 13ths this year.
Decade: 110s
110–119
Century: 2nd century
101–200
Millennium: 1st millennium
1–1000
Years ago: 1,913
1913 years before 2026.

In other calendars

Hebrew: 3873 / 3874 AM
Rosh Hashanah falls in September/October.
Chinese: Year of the zodiac:Water zodiac:Ox
Sexagenary cycle position 50 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 656 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: 105 / 106 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 35 / 34 Saka
Indian national calendar; year starts in March.

Properties

Parity: Odd
Digit count: 3
Digit sum: 5
Digit product: 3
Digital root: 5
Palindrome: No
Bit width: 7 bits
Reversed: 311
Recamán's sequence: a(34) = 113
Square (n²): 12,769
Cube (n³): 1,442,897
Divisor count: 2
σ(n) — sum of divisors: 114
φ(n) — Euler's totient: 112

Primality

113 is prime. It has exactly two divisors: 1 and itself.

Divisors & multiples

All divisors (2)

1 · 113

Aliquot sum (sum of proper divisors): 1

Factor pairs (a × b = 113)

1 × 113

First multiples

113 · 226 (double) · 339 · 452 · 565 · 678 · 791 · 904 · 1,017 · 1,130

Sums & aliquot sequence

As a sum of two squares: 7² + 8²

As consecutive integers: 56 + 57

Representations

In words: one hundred thirteen
Ordinal: 113th
Roman numeral: CXIII
Binary: 1110001
Octal: 161
Hexadecimal: 0x71
Base64: cQ==
One's complement: 142 (8-bit)

In other bases

ternary (3) 11012

quaternary (4) 1301

quinary (5) 423

senary (6) 305

septenary (7) 221

nonary (9) 135

undecimal (11) a3

duodecimal (12) 95

tridecimal (13) 89

tetradecimal (14) 81

pentadecimal (15) 78

Historical numeral systems

Babylonian (base 60): 𒁹 𒌋𒌋𒌋𒌋𒌋𒁹𒁹𒁹
Egyptian hieroglyphic: 𓍢𓎆𓏺𓏺𓏺
Greek (Milesian): ριγʹ
Mayan (base 20): 𝋥·𝋭
Chinese: 一百一十三
Chinese (financial): 壹佰壹拾參

In other modern scripts

Eastern Arabic ١١٣ Devanagari ११३ Bengali ১১৩ Tamil ௧௧௩ Thai ๑๑๓ Tibetan ༡༡༣ Khmer ១១៣ Lao ໑໑໓ Burmese ၁၁၃

Digit at this position in famous constants

π — Pi (π): Digit 113 = 2
e — Euler's number (e): Digit 113 = 0
φ — Golden ratio (φ): Digit 113 = 3
√2 — Pythagoras's (√2): Digit 113 = 9
ln 2 — Natural log of 2: Digit 113 = 5
γ — Euler-Mascheroni (γ): Digit 113 = 8

Also seen as

Prime neighborhood

Adjacent primes:

Previous prime: 109 (gap of 4)
Next prime: 127 (gap of 14)

Pair status: cousin with 109.

ASCII character

As an ASCII codepoint, 113 is q. Printable ASCII character q.

Hex color

#000071

RGB(0, 0, 113)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.0.113.

Address: 0.0.0.113
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.0.113

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