Live analysis

120,180

120,180 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.).

120,180 (one hundred twenty thousand one hundred eighty) is an even 6-digit number. It is a composite number with 24 divisors, and factors as 2² × 3 × 5 × 2,003. Its proper divisors sum to 216,492, more than the number itself, making it an abundant number. Written other ways, in hexadecimal, 0x1D574.

Abundant Number Arithmetic Number Cube-Free Evil Number Gapful Number Happy Number Harshad / Niven Semiperfect Number

Interestingness

★ ★ ★ ★ ☆

6 notable facts · grade B

120,168 120,169 120,170 120,171 120,172 120,173 120,174 120,175 120,176 120,177 120,178 120,179 120,180 120,181 120,182 120,183 120,184 120,185 120,186 120,187 120,188 120,189 120,190 120,191 120,192

less more

Properties

Parity: Even
Digit count: 6
Digit sum: 12
Digit product: 0
Digital root: 3
Palindrome: No
Bit width: 17 bits
Reversed: 81,021
Square (n²): 14,443,232,400
Cube (n³): 1,735,787,669,832,000
Divisor count: 24
σ(n) — sum of divisors: 336,672
φ(n) — Euler's totient: 32,032
Sum of prime factors: 2,015

Primality

Prime factorization: 2 ² × 3 × 5 × 2003

Nearest primes: 120,167 (−13) · 120,181 (+1)

Divisors & multiples

All divisors (24)

1 · 2 · 3 · 4 · 5 · 6 · 10 · 12 · 15 · 20 · 30 · 60 · 2003 · 4006 · 6009 · 8012 · 10015 · 12018 · 20030 · 24036 · 30045 · 40060 · 60090 (half) · 120180

Aliquot sum (sum of proper divisors): 216,492

Factor pairs (a × b = 120,180)

1 × 120180

2 × 60090

3 × 40060

4 × 30045

5 × 24036

6 × 20030

10 × 12018

12 × 10015

15 × 8012

20 × 6009

30 × 4006

60 × 2003

First multiples

120,180 · 240,360 (double) · 360,540 · 480,720 · 600,900 · 721,080 · 841,260 · 961,440 · 1,081,620 · 1,201,800

Sums & aliquot sequence

As consecutive integers: 40,059 + 40,060 + 40,061 24,034 + 24,035 + 24,036 + 24,037 + 24,038 15,019 + 15,020 + … + 15,026 8,005 + 8,006 + … + 8,019

Aliquot sequence: 120,180 → 216,492 → 288,684 → 537,960 → 1,076,280 → 2,152,920 → 5,934,120 → 11,868,600 → 25,450,440 → 51,791,160 → 104,628,840 → 226,317,720 → 452,635,800 → 988,529,400 → 2,473,377,000 → 5,243,568,600 → 11,011,495,920 — keeps growing

Continued fraction of √n

√120,180 = [346; (1, 2, 34, 2, 1, 692)]

Period length 6 — the block in parentheses repeats forever.

Representations

In words: one hundred twenty thousand one hundred eighty
Ordinal: 120180th
Binary: 11101010101110100
Octal: 352564
Hexadecimal: 0x1D574
Base64: AdV0
One's complement: 4,294,847,115 (32-bit)
Scientific notation: 1.2018 × 10⁵
As a duration: 120,180 s = 1 day, 9 hours, 23 minutes

In other bases

ternary (3) 20002212010

quaternary (4) 131111310

quinary (5) 12321210

senary (6) 2324220

septenary (7) 1010244

nonary (9) 202763

undecimal (11) 82325

duodecimal (12) 59670

tridecimal (13) 42918

tetradecimal (14) 31b24

pentadecimal (15) 25920

As an angle

120,180° = 333 × 360° + 300°

300° ≈ 5.236 rad

Compass bearing: WNW (west-northwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒌋𒌋𒁹𒁹𒁹 𒌋𒌋𒁹𒁹𒁹 ·
Egyptian hieroglyphic: 𓆐𓂍𓂍𓍢𓎆𓎆𓎆𓎆𓎆𓎆𓎆𓎆
Greek (Milesian): ͵ρκρπʹ
Mayan (base 20): 𝋯·𝋠·𝋩·𝋠
Chinese: 一十二萬零一百八十
Chinese (financial): 壹拾貳萬零壹佰捌拾

In other modern scripts

Eastern Arabic ١٢٠١٨٠ Devanagari १२०१८० Bengali ১২০১৮০ Tamil ௧௨௦௧௮௦ Thai ๑๒๐๑๘๐ Tibetan ༡༢༠༡༨༠ Khmer ១២០១៨០ Lao ໑໒໐໑໘໐ Burmese ၁၂၀၁၈၀

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 120180, here are decompositions:

13 + 120167 = 120180
17 + 120163 = 120180
23 + 120157 = 120180
59 + 120121 = 120180
83 + 120097 = 120180
89 + 120091 = 120180
101 + 120079 = 120180
103 + 120077 = 120180

Showing the first eight; more decompositions exist.

Unicode codepoint

𝕴

Mathematical Bold Fraktur Capital I

U+1D574

Uppercase letter (Lu)

UTF-8 encoding: F0 9D 95 B4 (4 bytes).

Lookup U+1D574 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#01D574

RGB(1, 213, 116)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.1.213.116.

Address: 0.1.213.116
Class: reserved
IPv4-mapped IPv6: ::ffff:0.1.213.116

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 120,180 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 US120,180 on Google Patents ↗ Look up on USPTO ↗

Position in π

The digit sequence 120180 first appears in π at position 413,366 of the decimal expansion (the 413,366ordinal-suffix:th 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 120180 on Pi Search ↗