Live analysis

120,960

120,960 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.).

120,960 (one hundred twenty thousand nine hundred sixty) is an even 6-digit number. It is a composite number with 128 divisors, and factors as 2⁷ × 3³ × 5 × 7. Its proper divisors sum to 368,640, more than the number itself, making it an abundant number. Written other ways, in hexadecimal, 0x1D880.

Abundant Number Arithmetic Number Evil Number Gapful Number Harshad / Niven Highly Abundant Practical Number Refactorable Number Weird Number

Interestingness

★ ★ ★ ★ ☆

7 notable facts · grade B

120,948 120,949 120,950 120,951 120,952 120,953 120,954 120,955 120,956 120,957 120,958 120,959 120,960 120,961 120,962 120,963 120,964 120,965 120,966 120,967 120,968 120,969 120,970 120,971 120,972

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Properties

Parity: Even
Digit count: 6
Digit sum: 18
Digit product: 0
Digital root: 9
Palindrome: No
Bit width: 17 bits
Reversed: 69,021
Square (n²): 14,631,321,600
Cube (n³): 1,769,804,660,736,000
Divisor count: 128
σ(n) — sum of divisors: 489,600
φ(n) — Euler's totient: 27,648
Sum of prime factors: 35

Primality

Prime factorization: 2 ⁷ × 3 ³ × 5 × 7

Nearest primes: 120,947 (−13) · 120,977 (+17)

Divisors & multiples

All divisors (128)

1 · 2 · 3 · 4 · 5 · 6 · 7 · 8 · 9 · 10 · 12 · 14 · 15 · 16 · 18 · 20 · 21 · 24 · 27 · 28 · 30 · 32 · 35 · 36 · 40 · 42 · 45 · 48 · 54 · 56 · 60 · 63 · 64 · 70 · 72 · 80 · 84 · 90 · 96 · 105 · 108 · 112 · 120 · 126 · 128 · 135 · 140 · 144 · 160 · 168 · 180 · 189 · 192 · 210 · 216 · 224 · 240 · 252 · 270 · 280 · 288 · 315 · 320 · 336 · 360 · 378 · 384 · 420 · 432 · 448 · 480 · 504 · 540 · 560 · 576 · 630 · 640 · 672 · 720 · 756 · 840 · 864 · 896 · 945 · 960 · 1008 · 1080 · 1120 · 1152 · 1260 · 1344 · 1440 · 1512 · 1680 · 1728 · 1890 · 1920 · 2016 · 2160 · 2240 · 2520 · 2688 · 2880 · 3024 · 3360 · 3456 · 3780 · 4032 · 4320 · 4480 · 5040 · 5760 · 6048 · 6720 · 7560 · 8064 · 8640 · 10080 · 12096 · 13440 · 15120 · 17280 · 20160 · 24192 · 30240 · 40320 · 60480 (half) · 120960

Aliquot sum (sum of proper divisors): 368,640

Factor pairs (a × b = 120,960)

1 × 120960

2 × 60480

3 × 40320

4 × 30240

5 × 24192

6 × 20160

7 × 17280

8 × 15120

9 × 13440

10 × 12096

12 × 10080

14 × 8640

15 × 8064

16 × 7560

18 × 6720

20 × 6048

21 × 5760

24 × 5040

27 × 4480

28 × 4320

30 × 4032

32 × 3780

35 × 3456

36 × 3360

40 × 3024

42 × 2880

45 × 2688

48 × 2520

54 × 2240

56 × 2160

60 × 2016

63 × 1920

64 × 1890

70 × 1728

72 × 1680

80 × 1512

84 × 1440

90 × 1344

96 × 1260

105 × 1152

108 × 1120

112 × 1080

120 × 1008

126 × 960

128 × 945

135 × 896

140 × 864

144 × 840

160 × 756

168 × 720

180 × 672

189 × 640

192 × 630

210 × 576

216 × 560

224 × 540

240 × 504

252 × 480

270 × 448

280 × 432

288 × 420

315 × 384

320 × 378

336 × 360

First multiples

120,960 · 241,920 (double) · 362,880 · 483,840 · 604,800 · 725,760 · 846,720 · 967,680 · 1,088,640 · 1,209,600

Sums & aliquot sequence

As consecutive integers: 40,319 + 40,320 + 40,321 24,190 + 24,191 + 24,192 + 24,193 + 24,194 17,277 + 17,278 + … + 17,283 13,436 + 13,437 + … + 13,444

Aliquot sequence: 120,960 → 368,640 → 909,234 → 1,060,812 → 1,661,908 → 1,246,438 → 721,682 → 474,310 → 379,466 → 189,736 → 176,204 → 206,836 → 216,524 → 294,196 → 344,204 → 381,556 → 381,612 — unresolved within range

Continued fraction of √n

√120,960 = [347; (1, 3, 1, 4, 1, 18, 2, 42, 1, 76, 3, 4, 2, 173, 2, 4, 3, 76, 1, 42, 2, 18, 1, 4, …)]

Period length 28 — the block in parentheses repeats forever.

Representations

In words: one hundred twenty thousand nine hundred sixty
Ordinal: 120960th
Binary: 11101100010000000
Octal: 354200
Hexadecimal: 0x1D880
Base64: AdiA
One's complement: 4,294,846,335 (32-bit)
Scientific notation: 1.2096 × 10⁵
As a duration: 120,960 s = 1 day, 9 hours, 36 minutes

In other bases

ternary (3) 20010221000

quaternary (4) 131202000

quinary (5) 12332320

senary (6) 2332000

septenary (7) 1012440

nonary (9) 203830

undecimal (11) 82974

duodecimal (12) 5a000

tridecimal (13) 43098

tetradecimal (14) 32120

pentadecimal (15) 25c90

As an angle

120,960° = 336 × 360°

0° ≈ 0 rad

Compass bearing: N (north)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒌋𒌋𒁹𒁹𒁹 𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹 ·
Egyptian hieroglyphic: 𓆐𓂍𓂍𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓎆𓎆𓎆𓎆𓎆𓎆
Greek (Milesian): ͵ρκϡξʹ
Mayan (base 20): 𝋯·𝋢·𝋨·𝋠
Chinese: 一十二萬零九百六十
Chinese (financial): 壹拾貳萬零玖佰陸拾

In other modern scripts

Eastern Arabic ١٢٠٩٦٠ Devanagari १२०९६० Bengali ১২০৯৬০ Tamil ௧௨௦௯௬௦ Thai ๑๒๐๙๖๐ Tibetan ༡༢༠༩༦༠ Khmer ១២០៩៦០ Lao ໑໒໐໙໖໐ Burmese ၁၂၀၉၆၀

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 120960, here are decompositions:

13 + 120947 = 120960
17 + 120943 = 120960
19 + 120941 = 120960
23 + 120937 = 120960
31 + 120929 = 120960
41 + 120919 = 120960
43 + 120917 = 120960
53 + 120907 = 120960

Showing the first eight; more decompositions exist.

Unicode codepoint

𝢀

Signwriting Hand-Hinge Thumb Side

U+1D880

Other symbol (So)

UTF-8 encoding: F0 9D A2 80 (4 bytes).

Lookup U+1D880 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#01D880

RGB(1, 216, 128)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.1.216.128.

Address: 0.1.216.128
Class: reserved
IPv4-mapped IPv6: ::ffff:0.1.216.128

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 120,960 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 US120,960 on Google Patents ↗ Look up on USPTO ↗