Live analysis

120,072

120,072 is a composite number, even.

This number doesn't have a permanent NumberWiki page yet — what you see below is computed live. Pages get added to the permanent index when they're notable (years, primes, curated, etc.).

120,072 (one hundred twenty thousand seventy-two) is an even 6-digit number. It is a composite number with 16 divisors, and factors as 2³ × 3 × 5,003. Its proper divisors sum to 180,168, more than the number itself, making it an abundant number. Written other ways, in hexadecimal, 0x1D508.

Abundant Number Arithmetic Number Gapful Number Harshad / Niven Odious Number Pernicious Number Recamán's Sequence Semiperfect Number

Interestingness

★ ★ ★ ☆ ☆

5 notable facts · grade C

120,060 120,061 120,062 120,063 120,064 120,065 120,066 120,067 120,068 120,069 120,070 120,071 120,072 120,073 120,074 120,075 120,076 120,077 120,078 120,079 120,080 120,081 120,082 120,083 120,084

less more

Properties

Parity: Even
Digit count: 6
Digit sum: 12
Digit product: 0
Digital root: 3
Palindrome: No
Bit width: 17 bits
Reversed: 270,021
Recamán's sequence: a(239,952) = 120,072
Square (n²): 14,417,285,184
Cube (n³): 1,731,112,266,613,248
Divisor count: 16
σ(n) — sum of divisors: 300,240
φ(n) — Euler's totient: 40,016
Sum of prime factors: 5,012

Primality

Prime factorization: 2 ³ × 3 × 5003

Nearest primes: 120,067 (−5) · 120,077 (+5)

Divisors & multiples

All divisors (16)

1 · 2 · 3 · 4 · 6 · 8 · 12 · 24 · 5003 · 10006 · 15009 · 20012 · 30018 · 40024 · 60036 (half) · 120072

Aliquot sum (sum of proper divisors): 180,168

Factor pairs (a × b = 120,072)

1 × 120072

2 × 60036

3 × 40024

4 × 30018

6 × 20012

8 × 15009

12 × 10006

24 × 5003

First multiples

120,072 · 240,144 (double) · 360,216 · 480,288 · 600,360 · 720,432 · 840,504 · 960,576 · 1,080,648 · 1,200,720

Sums & aliquot sequence

As consecutive integers: 40,023 + 40,024 + 40,025 7,497 + 7,498 + … + 7,512 2,478 + 2,479 + … + 2,525

Aliquot sequence: 120,072 → 180,168 → 270,312 → 502,488 → 1,054,392 → 1,581,648 → 2,563,920 → 6,274,800 → 19,556,880 → 51,010,032 → 81,744,864 → 133,316,976 → 237,579,424 → 230,554,676 → 209,595,244 → 188,252,780 → 207,885,172 — unresolved within range

Continued fraction of √n

√120,072 = [346; (1, 1, 17, 3, 1, 2, 2, 3, 1, 2, 9, 1, 4, 1, 11, 1, 1, 5, 14, 1, 1, 3, 2, 1, …)]

Representations

In words: one hundred twenty thousand seventy-two
Ordinal: 120072nd
Binary: 11101010100001000
Octal: 352410
Hexadecimal: 0x1D508
Base64: AdUI
One's complement: 4,294,847,223 (32-bit)
Scientific notation: 1.20072 × 10⁵
As a duration: 120,072 s = 1 day, 9 hours, 21 minutes, 12 seconds

In other bases

ternary (3) 20002201010

quaternary (4) 131110020

quinary (5) 12320242

senary (6) 2323520

septenary (7) 1010031

nonary (9) 202633

undecimal (11) 82237

duodecimal (12) 595a0

tridecimal (13) 42864

tetradecimal (14) 31a88

pentadecimal (15) 2589c

As an angle

120,072° = 333 × 360° + 192°

192° ≈ 3.351 rad

Compass bearing: SSW (south-southwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒌋𒌋𒁹𒁹𒁹 𒌋𒌋𒁹 𒌋𒁹𒁹
Egyptian hieroglyphic: 𓆐𓂍𓂍𓎆𓎆𓎆𓎆𓎆𓎆𓎆𓏺𓏺
Greek (Milesian): ͵ρκοβʹ
Mayan (base 20): 𝋯·𝋠·𝋣·𝋬
Chinese: 一十二萬零七十二
Chinese (financial): 壹拾貳萬零柒拾貳

In other modern scripts

Eastern Arabic ١٢٠٠٧٢ Devanagari १२००७२ Bengali ১২০০৭২ Tamil ௧௨௦௦௭௨ Thai ๑๒๐๐๗๒ Tibetan ༡༢༠༠༧༢ Khmer ១២០០៧២ Lao ໑໒໐໐໗໒ Burmese ၁၂၀၀၇၂

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 120072, here are decompositions:

5 + 120067 = 120072
23 + 120049 = 120072
31 + 120041 = 120072
61 + 120011 = 120072
79 + 119993 = 120072
89 + 119983 = 120072
101 + 119971 = 120072
109 + 119963 = 120072

Showing the first eight; more decompositions exist.

Unicode codepoint

𝔈

Mathematical Fraktur Capital E

U+1D508

Uppercase letter (Lu)

UTF-8 encoding: F0 9D 94 88 (4 bytes).

Lookup U+1D508 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#01D508

RGB(1, 213, 8)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.1.213.8.

Address: 0.1.213.8
Class: reserved
IPv4-mapped IPv6: ::ffff:0.1.213.8

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

Possible US patent number

This number falls in the range of US utility patent numbers. If it's a patent, it would be issued as US 120,072 and was likely granted around 1871.

Patent numbers below 100,000 are excluded as too ambiguous; modern numbering currently reaches roughly 12.5 million.

Look up US120,072 on Google Patents ↗ Look up on USPTO ↗

Position in π

The digit sequence 120072 first appears in π at position 779,771 of the decimal expansion (the 779,771ordinal-suffix:st digit after the integer 3).

Search range: the first 1,000,000 fractional digits of π. Any 6-digit-or-shorter string is virtually guaranteed to appear in there — the more interesting signal is the position.

Look up 120072 on Pi Search ↗