Live analysis

120,240

120,240 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.).

120,240 (one hundred twenty thousand two hundred forty) is an even 6-digit number. It is a composite number with 60 divisors, and factors as 2⁴ × 3² × 5 × 167. Its proper divisors sum to 285,984, more than the number itself, making it an abundant number. Written other ways, in hexadecimal, 0x1D5B0.

Abundant Number Gapful Number Harshad / Niven Odious Number Practical Number Refactorable Number Semiperfect Number

Interestingness

★ ★ ★ ☆ ☆

5 notable facts · grade C

120,228 120,229 120,230 120,231 120,232 120,233 120,234 120,235 120,236 120,237 120,238 120,239 120,240 120,241 120,242 120,243 120,244 120,245 120,246 120,247 120,248 120,249 120,250 120,251 120,252

less more

Properties

Parity: Even
Digit count: 6
Digit sum: 9
Digit product: 0
Digital root: 9
Palindrome: No
Bit width: 17 bits
Reversed: 42,021
Square (n²): 14,457,657,600
Cube (n³): 1,738,388,749,824,000
Divisor count: 60
σ(n) — sum of divisors: 406,224
φ(n) — Euler's totient: 31,872
Sum of prime factors: 186

Primality

Prime factorization: 2 ⁴ × 3 ² × 5 × 167

Nearest primes: 120,233 (−7) · 120,247 (+7)

Divisors & multiples

All divisors (60)

1 · 2 · 3 · 4 · 5 · 6 · 8 · 9 · 10 · 12 · 15 · 16 · 18 · 20 · 24 · 30 · 36 · 40 · 45 · 48 · 60 · 72 · 80 · 90 · 120 · 144 · 167 · 180 · 240 · 334 · 360 · 501 · 668 · 720 · 835 · 1002 · 1336 · 1503 · 1670 · 2004 · 2505 · 2672 · 3006 · 3340 · 4008 · 5010 · 6012 · 6680 · 7515 · 8016 · 10020 · 12024 · 13360 · 15030 · 20040 · 24048 · 30060 · 40080 · 60120 (half) · 120240

Aliquot sum (sum of proper divisors): 285,984

Factor pairs (a × b = 120,240)

1 × 120240

2 × 60120

3 × 40080

4 × 30060

5 × 24048

6 × 20040

8 × 15030

9 × 13360

10 × 12024

12 × 10020

15 × 8016

16 × 7515

18 × 6680

20 × 6012

24 × 5010

30 × 4008

36 × 3340

40 × 3006

45 × 2672

48 × 2505

60 × 2004

72 × 1670

80 × 1503

90 × 1336

120 × 1002

144 × 835

167 × 720

180 × 668

240 × 501

334 × 360

First multiples

120,240 · 240,480 (double) · 360,720 · 480,960 · 601,200 · 721,440 · 841,680 · 961,920 · 1,082,160 · 1,202,400

Sums & aliquot sequence

As consecutive integers: 40,079 + 40,080 + 40,081 24,046 + 24,047 + 24,048 + 24,049 + 24,050 13,356 + 13,357 + … + 13,364 8,009 + 8,010 + … + 8,023

Aliquot sequence: 120,240 → 285,984 → 550,656 → 1,043,664 → 1,813,296 → 3,002,368 → 3,009,826 → 1,785,374 → 1,050,274 → 525,140 → 904,876 → 1,012,340 → 1,463,056 → 1,776,816 → 3,391,256 → 3,639,544 → 3,184,616 — unresolved within range

Continued fraction of √n

√120,240 = [346; (1, 3, 9, 1, 1, 13, 1, 1, 1, 2, 5, 2, 4, 1, 2, 8, 4, 1, 5, 43, 5, 1, 4, 8, …)]

Period length 40 — the block in parentheses repeats forever.

Representations

In words: one hundred twenty thousand two hundred forty
Ordinal: 120240th
Binary: 11101010110110000
Octal: 352660
Hexadecimal: 0x1D5B0
Base64: AdWw
One's complement: 4,294,847,055 (32-bit)
Scientific notation: 1.2024 × 10⁵
As a duration: 120,240 s = 1 day, 9 hours, 24 minutes

In other bases

ternary (3) 20002221100

quaternary (4) 131112300

quinary (5) 12321430

senary (6) 2324400

septenary (7) 1010361

nonary (9) 202840

undecimal (11) 8237a

duodecimal (12) 59700

tridecimal (13) 42963

tetradecimal (14) 31b68

pentadecimal (15) 25960

As an angle

120,240° = 334 × 360°

0° ≈ 0 rad

Compass bearing: N (north)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒌋𒌋𒁹𒁹𒁹 𒌋𒌋𒁹𒁹𒁹𒁹 ·
Egyptian hieroglyphic: 𓆐𓂍𓂍𓍢𓍢𓎆𓎆𓎆𓎆
Greek (Milesian): ͵ρκσμʹ
Mayan (base 20): 𝋯·𝋠·𝋬·𝋠
Chinese: 一十二萬零二百四十
Chinese (financial): 壹拾貳萬零貳佰肆拾

In other modern scripts

Eastern Arabic ١٢٠٢٤٠ Devanagari १२०२४० Bengali ১২০২৪০ Tamil ௧௨௦௨௪௦ Thai ๑๒๐๒๔๐ Tibetan ༡༢༠༢༤༠ Khmer ១២០២៤០ Lao ໑໒໐໒໔໐ Burmese ၁၂၀၂၄၀

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 120240, here are decompositions:

7 + 120233 = 120240
17 + 120223 = 120240
31 + 120209 = 120240
41 + 120199 = 120240
47 + 120193 = 120240
59 + 120181 = 120240
73 + 120167 = 120240
83 + 120157 = 120240

Showing the first eight; more decompositions exist.

Unicode codepoint

𝖰

Mathematical Sans-Serif Capital Q

U+1D5B0

Uppercase letter (Lu)

UTF-8 encoding: F0 9D 96 B0 (4 bytes).

Lookup U+1D5B0 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#01D5B0

RGB(1, 213, 176)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.1.213.176.

Address: 0.1.213.176
Class: reserved
IPv4-mapped IPv6: ::ffff:0.1.213.176

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 120,240 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 US120,240 on Google Patents ↗ Look up on USPTO ↗

Position in π

The digit sequence 120240 first appears in π at position 456,455 of the decimal expansion (the 456,455ordinal-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 120240 on Pi Search ↗