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120,120

120,120 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.).

120,120 (one hundred twenty thousand one hundred twenty) is an even 6-digit number. It is a composite number with 128 divisors, and factors as 2³ × 3 × 5 × 7 × 11 × 13. Its proper divisors sum to 363,720, more than the number itself, making it an abundant number. Written other ways, in hexadecimal, 0x1D538.

Abundant Number Arithmetic Number Gapful Number Happy Number Harshad / Niven Highly Abundant Odious Number Practical Number Recamán's Sequence Weird Number

Interestingness

Properties

Parity
Even
Digit count
6
Digit sum
6
Digit product
0
Digital root
6
Palindrome
No
Bit width
17 bits
Reversed
21,021
Recamán's sequence
a(239,856) = 120,120
Square (n²)
14,428,814,400
Cube (n³)
1,733,189,185,728,000
Divisor count
128
σ(n) — sum of divisors
483,840
φ(n) — Euler's totient
23,040
Sum of prime factors
45

Primality

Prime factorization: 2 3 × 3 × 5 × 7 × 11 × 13

Nearest primes: 120,103 (−17) · 120,121 (+1)

Divisors & multiples

All divisors (128)
1 · 2 · 3 · 4 · 5 · 6 · 7 · 8 · 10 · 11 · 12 · 13 · 14 · 15 · 20 · 21 · 22 · 24 · 26 · 28 · 30 · 33 · 35 · 39 · 40 · 42 · 44 · 52 · 55 · 56 · 60 · 65 · 66 · 70 · 77 · 78 · 84 · 88 · 91 · 104 · 105 · 110 · 120 · 130 · 132 · 140 · 143 · 154 · 156 · 165 · 168 · 182 · 195 · 210 · 220 · 231 · 260 · 264 · 273 · 280 · 286 · 308 · 312 · 330 · 364 · 385 · 390 · 420 · 429 · 440 · 455 · 462 · 520 · 546 · 572 · 616 · 660 · 715 · 728 · 770 · 780 · 840 · 858 · 910 · 924 · 1001 · 1092 · 1144 · 1155 · 1320 · 1365 · 1430 · 1540 · 1560 · 1716 · 1820 · 1848 · 2002 · 2145 · 2184 · 2310 · 2730 · 2860 · 3003 · 3080 · 3432 · 3640 · 4004 · 4290 · 4620 · 5005 · 5460 · 5720 · 6006 · 8008 · 8580 · 9240 · 10010 · 10920 · 12012 · 15015 · 17160 · 20020 · 24024 · 30030 · 40040 · 60060 (half) · 120120
Aliquot sum (sum of proper divisors): 363,720
Factor pairs (a × b = 120,120)
1 × 120120
2 × 60060
3 × 40040
4 × 30030
5 × 24024
6 × 20020
7 × 17160
8 × 15015
10 × 12012
11 × 10920
12 × 10010
13 × 9240
14 × 8580
15 × 8008
20 × 6006
21 × 5720
22 × 5460
24 × 5005
26 × 4620
28 × 4290
30 × 4004
33 × 3640
35 × 3432
39 × 3080
40 × 3003
42 × 2860
44 × 2730
52 × 2310
55 × 2184
56 × 2145
60 × 2002
65 × 1848
66 × 1820
70 × 1716
77 × 1560
78 × 1540
84 × 1430
88 × 1365
91 × 1320
104 × 1155
105 × 1144
110 × 1092
120 × 1001
130 × 924
132 × 910
140 × 858
143 × 840
154 × 780
156 × 770
165 × 728
168 × 715
182 × 660
195 × 616
210 × 572
220 × 546
231 × 520
260 × 462
264 × 455
273 × 440
280 × 429
286 × 420
308 × 390
312 × 385
330 × 364
First multiples
120,120 · 240,240 (double) · 360,360 · 480,480 · 600,600 · 720,720 · 840,840 · 960,960 · 1,081,080 · 1,201,200

Sums & aliquot sequence

As consecutive integers: 40,039 + 40,040 + 40,041 24,022 + 24,023 + 24,024 + 24,025 + 24,026 17,157 + 17,158 + … + 17,163 10,915 + 10,916 + … + 10,925
Aliquot sequence: 120,120 363,720 886,200 2,268,360 5,104,980 10,619,820 22,402,260 49,558,356 75,714,246 89,961,498 122,675,238 194,306,778 227,132,838 266,373,162 365,213,430 584,341,722 714,195,558 — unresolved within range

Continued fraction of √n

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

Period length 6 — the block in parentheses repeats forever.

Representations

In words
one hundred twenty thousand one hundred twenty
Ordinal
120120th
Binary
11101010100111000
Octal
352470
Hexadecimal
0x1D538
Base64
AdU4
One's complement
4,294,847,175 (32-bit)
Scientific notation
1.2012 × 10⁵
As a duration
120,120 s = 1 day, 9 hours, 22 minutes
In other bases
ternary (3) 20002202220
quaternary (4) 131110320
quinary (5) 12320440
senary (6) 2324040
septenary (7) 1010130
nonary (9) 202686
undecimal (11) 82280
duodecimal (12) 59620
tridecimal (13) 428a0
tetradecimal (14) 31ac0
pentadecimal (15) 258d0

As an angle

120,120° = 333 × 360° + 240°
240° ≈ 4.189 rad
Compass bearing: WSW (west-southwest)

Historical numeral systems

Babylonian (base 60)
𒌋𒌋𒌋𒁹𒁹𒁹 𒌋𒌋𒁹𒁹 ·
Egyptian hieroglyphic
𓆐𓂍𓂍𓍢𓎆𓎆
Greek (Milesian)
͵ρκρκʹ
Mayan (base 20)
𝋯·𝋠·𝋦·𝋠
Chinese
一十二萬零一百二十
Chinese (financial)
壹拾貳萬零壹佰貳拾
In other modern scripts
Eastern Arabic ١٢٠١٢٠ Devanagari १२०१२० Bengali ১২০১২০ Tamil ௧௨௦௧௨௦ Thai ๑๒๐๑๒๐ Tibetan ༡༢༠༡༢༠ Khmer ១២០១២០ Lao ໑໒໐໑໒໐ Burmese ၁၂၀၁၂၀

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 120120, here are decompositions:

  • 17 + 120103 = 120120
  • 23 + 120097 = 120120
  • 29 + 120091 = 120120
  • 41 + 120079 = 120120
  • 43 + 120077 = 120120
  • 53 + 120067 = 120120
  • 71 + 120049 = 120120
  • 73 + 120047 = 120120

Showing the first eight; more decompositions exist.

Unicode codepoint
𝔸
Mathematical Double-Struck Capital A
U+1D538
Uppercase letter (Lu)

UTF-8 encoding: F0 9D 94 B8 (4 bytes).

Hex color
#01D538
RGB(1, 213, 56)
IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.1.213.56.

Address
0.1.213.56
Class
reserved
IPv4-mapped IPv6
::ffff:0.1.213.56

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 120,120 and was likely granted around 1871.

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

Position in π

The digit sequence 120120 first appears in π at position 87,600 of the decimal expansion (the 87,600ordinal-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.

Related reading

  • Babylonian numerals — The base-60 cuneiform system that gave us 60 minutes, 60 seconds, and 360°.