Live analysis

105,120

105,120 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.).

105,120 (one hundred five thousand one hundred twenty) is an even 6-digit number. It is a composite number with 72 divisors, and factors as 2⁵ × 3² × 5 × 73. Its proper divisors sum to 258,516, more than the number itself, making it an abundant number. Written other ways, in hexadecimal, 0x19AA0.

Abundant Number Gapful Number Happy Number Harshad / Niven Odious Number Pernicious Number Practical Number Recamán's Sequence Refactorable Number Weird Number

Interestingness

★ ★ ★ ★ ☆

7 notable facts · grade B

105,108 105,109 105,110 105,111 105,112 105,113 105,114 105,115 105,116 105,117 105,118 105,119 105,120 105,121 105,122 105,123 105,124 105,125 105,126 105,127 105,128 105,129 105,130 105,131 105,132

less more

Properties

Parity: Even
Digit count: 6
Digit sum: 9
Digit product: 0
Digital root: 9
Palindrome: No
Bit width: 17 bits
Reversed: 21,501
Recamán's sequence: a(90,843) = 105,120
Square (n²): 11,050,214,400
Cube (n³): 1,161,598,537,728,000
Divisor count: 72
σ(n) — sum of divisors: 363,636
φ(n) — Euler's totient: 27,648
Sum of prime factors: 94

Primality

Prime factorization: 2 ⁵ × 3 ² × 5 × 73

Nearest primes: 105,107 (−13) · 105,137 (+17)

Divisors & multiples

All divisors (72)

1 · 2 · 3 · 4 · 5 · 6 · 8 · 9 · 10 · 12 · 15 · 16 · 18 · 20 · 24 · 30 · 32 · 36 · 40 · 45 · 48 · 60 · 72 · 73 · 80 · 90 · 96 · 120 · 144 · 146 · 160 · 180 · 219 · 240 · 288 · 292 · 360 · 365 · 438 · 480 · 584 · 657 · 720 · 730 · 876 · 1095 · 1168 · 1314 · 1440 · 1460 · 1752 · 2190 · 2336 · 2628 · 2920 · 3285 · 3504 · 4380 · 5256 · 5840 · 6570 · 7008 · 8760 · 10512 · 11680 · 13140 · 17520 · 21024 · 26280 · 35040 · 52560 (half) · 105120

Aliquot sum (sum of proper divisors): 258,516

Factor pairs (a × b = 105,120)

1 × 105120

2 × 52560

3 × 35040

4 × 26280

5 × 21024

6 × 17520

8 × 13140

9 × 11680

10 × 10512

12 × 8760

15 × 7008

16 × 6570

18 × 5840

20 × 5256

24 × 4380

30 × 3504

32 × 3285

36 × 2920

40 × 2628

45 × 2336

48 × 2190

60 × 1752

72 × 1460

73 × 1440

80 × 1314

90 × 1168

96 × 1095

120 × 876

144 × 730

146 × 720

160 × 657

180 × 584

219 × 480

240 × 438

288 × 365

292 × 360

First multiples

105,120 · 210,240 (double) · 315,360 · 420,480 · 525,600 · 630,720 · 735,840 · 840,960 · 946,080 · 1,051,200

Sums & aliquot sequence

As a sum of two squares: 12² + 324² = 204² + 252²

As consecutive integers: 35,039 + 35,040 + 35,041 21,022 + 21,023 + 21,024 + 21,025 + 21,026 11,676 + 11,677 + … + 11,684 7,001 + 7,002 + … + 7,015

Aliquot sequence: 105,120 → 258,516 → 414,156 → 552,236 → 414,184 → 396,536 → 473,704 → 635,096 → 850,984 → 744,626 → 372,316 → 372,372 → 831,852 → 1,572,004 → 1,710,044 → 1,740,676 → 1,879,052 — unresolved within range

Continued fraction of √n

√105,120 = [324; (4, 1, 1, 161, 1, 1, 4, 648)]

Period length 8 — the block in parentheses repeats forever.

Representations

In words: one hundred five thousand one hundred twenty
Ordinal: 105120th
Binary: 11001101010100000
Octal: 315240
Hexadecimal: 0x19AA0
Base64: AZqg
One's complement: 4,294,862,175 (32-bit)
Scientific notation: 1.0512 × 10⁵
As a duration: 105,120 s = 1 day, 5 hours, 12 minutes

In other bases

ternary (3) 12100012100

quaternary (4) 121222200

quinary (5) 11330440

senary (6) 2130400

septenary (7) 615321

nonary (9) 170170

undecimal (11) 71a84

duodecimal (12) 50a00

tridecimal (13) 38b02

tetradecimal (14) 2a448

pentadecimal (15) 21230

As an angle

105,120° = 292 × 360°

0° ≈ 0 rad

Compass bearing: N (north)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒁹𒁹 ·
Egyptian hieroglyphic: 𓆐𓆼𓆼𓆼𓆼𓆼𓍢𓎆𓎆
Greek (Milesian): ͵ρερκʹ
Mayan (base 20): 𝋭·𝋢·𝋰·𝋠
Chinese: 一十萬五千一百二十
Chinese (financial): 壹拾萬伍仟壹佰貳拾

In other modern scripts

Eastern Arabic ١٠٥١٢٠ Devanagari १०५१२० Bengali ১০৫১২০ Tamil ௧௦௫௧௨௦ Thai ๑๐๕๑๒๐ Tibetan ༡༠༥༡༢༠ Khmer ១០៥១២០ Lao ໑໐໕໑໒໐ Burmese ၁၀၅၁၂၀

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 105120, here are decompositions:

13 + 105107 = 105120
23 + 105097 = 105120
83 + 105037 = 105120
89 + 105031 = 105120
97 + 105023 = 105120
101 + 105019 = 105120
149 + 104971 = 105120
167 + 104953 = 105120

Showing the first eight; more decompositions exist.

Hex color

#019AA0

RGB(1, 154, 160)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.1.154.160.

Address: 0.1.154.160
Class: reserved
IPv4-mapped IPv6: ::ffff:0.1.154.160

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 105,120 and was likely granted around 1870.

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

Look up US105,120 on Google Patents ↗ Look up on USPTO ↗

Position in π

The digit sequence 105120 first appears in π at position 437,817 of the decimal expansion (the 437,817ordinal-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 105120 on Pi Search ↗