Number

126

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

126 (one hundred twenty-six) is an even 3-digit number. It is a composite number with 12 divisors, and factors as 2 × 3² × 7. Its proper divisors sum to 186, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is CXXVI and in binary, 1111110.

Abundant Number Arithmetic Number Ascending Digits Cube-Free Decagonal Evil Number Harshad / Niven Pentagonal Pyramidal Pentatope Number Practical Number Recamán's Sequence Semiperfect Number Year

Interestingness

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10 notable facts · grade A

114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138

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Historical context — 126 AD

Calendar year

Year 126 (CXXVI) was a common year starting on Monday of the Julian calendar.

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

Historical context — 126 BC

Calendar year

Year 126 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: Tuesday
January 1, 126
Ended on: Tuesday
December 31, 126
Friday the 13ths: 2
2 Friday the 13ths this year.
Decade: 120s
120–129
Century: 2nd century
101–200
Millennium: 1st millennium
1–1000
Years ago: 1,900
1900 years before 2026.

In other calendars

Hebrew: 3886 / 3887 AM
Rosh Hashanah falls in September/October.
Chinese: Year of the zodiac:Fire zodiac:Tiger
Sexagenary cycle position 3 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 669 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: 118 / 119 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 48 / 47 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 3
Digit sum: 9
Digit product: 12
Digital root: 9
Palindrome: No
Bit width: 7 bits
Reversed: 621
Recamán's sequence: a(148) = 126
Square (n²): 15,876
Cube (n³): 2,000,376
Divisor count: 12
σ(n) — sum of divisors: 312
φ(n) — Euler's totient: 36
Sum of prime factors: 15

Primality

Prime factorization: 2 × 3 ² × 7

Nearest primes: 113 (−13) · 127 (+1)

Divisors & multiples

All divisors (12)

1 · 2 · 3 · 6 · 7 · 9 · 14 · 18 · 21 · 42 · 63 (half) · 126

Aliquot sum (sum of proper divisors): 186

Factor pairs (a × b = 126)

1 × 126

2 × 63

3 × 42

6 × 21

7 × 18

9 × 14

First multiples

126 · 252 (double) · 378 · 504 · 630 · 756 · 882 · 1,008 · 1,134 · 1,260

Sums & aliquot sequence

As a sum of two cubes: 1³ + 5³

As consecutive integers: 41 + 42 + 43 30 + 31 + 32 + 33 15 + 16 + … + 21 10 + 11 + … + 18

Aliquot sequence: 126 → 186 → 198 → 270 → 450 → 759 → 393 → 135 → 105 → 87 → 33 → 15 → 9 → 4 → 3 → 1 → 0 — terminates at zero

Continued fraction of √n

√126 = [11; (4, 2, 4, 22)]

Period length 4 — the block in parentheses repeats forever.

Representations

In words: one hundred twenty-six
Ordinal: 126th
Roman numeral: CXXVI
Binary: 1111110
Octal: 176
Hexadecimal: 0x7E
Base64: fg==
One's complement: 129 (8-bit)
Scientific notation: 1.26 × 10²
As a duration: 126 s = 2 minutes, 6 seconds

In other bases

ternary (3) 11200

quaternary (4) 1332

quinary (5) 1001

senary (6) 330

septenary (7) 240

nonary (9) 150

undecimal (11) 105

duodecimal (12) a6

tridecimal (13) 99

tetradecimal (14) 90

pentadecimal (15) 86

Palindromic in base 5

As an angle

126°

126° ≈ 2.199 rad

Compass bearing: SE (southeast)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹 𒁹𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓍢𓎆𓎆𓏺𓏺𓏺𓏺𓏺𓏺
Greek (Milesian): ρκϛʹ
Mayan (base 20): 𝋦·𝋦
Chinese: 一百二十六
Chinese (financial): 壹佰貳拾陸

In other modern scripts

Eastern Arabic ١٢٦ Devanagari १२६ Bengali ১২৬ Tamil ௧௨௬ Thai ๑๒๖ Tibetan ༡༢༦ Khmer ១២៦ Lao ໑໒໖ Burmese ၁၂၆

Digit at this position in famous constants

π — Pi (π): Digit 126 = 4
e — Euler's number (e): Digit 126 = 1
φ — Golden ratio (φ): Digit 126 = 3
√2 — Pythagoras's (√2): Digit 126 = 3
ln 2 — Natural log of 2: Digit 126 = 2
γ — Euler-Mascheroni (γ): Digit 126 = 0

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 126, here are decompositions:

13 + 113 = 126
17 + 109 = 126
19 + 107 = 126
23 + 103 = 126
29 + 97 = 126
37 + 89 = 126
43 + 83 = 126
47 + 79 = 126

Showing the first eight; more decompositions exist.

ASCII character

As an ASCII codepoint, 126 is ~. Printable ASCII character ~.

Hex color

#00007E

RGB(0, 0, 126)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.0.126.

Address: 0.0.0.126
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.0.126

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

Musical pitch

Heard as a frequency, 126 Hz is closest to:

Concert pitch (A4 = 440 Hz): B2 (123.5 Hz, +35¢)
Scientific pitch (C4 = 256 Hz): C3 (128 Hz, -27¢)
Baroque pitch (A4 = 415 Hz): C3 (123.4 Hz, +36¢)

As a MIDI note number, 126 is F♯9 (11839.8 Hz at concert pitch).