Live analysis

100,100

100,100 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.).

100,100 (one hundred thousand one hundred) is an even 6-digit number. It is a composite number with 72 divisors, and factors as 2² × 5² × 7 × 11 × 13. Its proper divisors sum to 191,548, more than the number itself, making it an abundant number. Written other ways, in hexadecimal, 0x18704.

Abundant Number Cube-Free Evil Number Flippable Gapful Number Harshad / Niven Practical Number Weird Number

Interestingness

★ ★ ★ ★ ☆

6 notable facts · grade B

100,088 100,089 100,090 100,091 100,092 100,093 100,094 100,095 100,096 100,097 100,098 100,099 100,100 100,101 100,102 100,103 100,104 100,105 100,106 100,107 100,108 100,109 100,110 100,111 100,112

less more

Properties

Parity: Even
Digit count: 6
Digit sum: 2
Digit product: 0
Digital root: 2
Palindrome: No
Bit width: 17 bits
Reversed: 1,001
Flips to (rotate 180°): 1,001
Square (n²): 10,020,010,000
Cube (n³): 1,003,003,001,000,000
Divisor count: 72
σ(n) — sum of divisors: 291,648
φ(n) — Euler's totient: 28,800
Sum of prime factors: 45

Primality

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

Nearest primes: 100,069 (−31) · 100,103 (+3)

Divisors & multiples

All divisors (72)

1 · 2 · 4 · 5 · 7 · 10 · 11 · 13 · 14 · 20 · 22 · 25 · 26 · 28 · 35 · 44 · 50 · 52 · 55 · 65 · 70 · 77 · 91 · 100 · 110 · 130 · 140 · 143 · 154 · 175 · 182 · 220 · 260 · 275 · 286 · 308 · 325 · 350 · 364 · 385 · 455 · 550 · 572 · 650 · 700 · 715 · 770 · 910 · 1001 · 1100 · 1300 · 1430 · 1540 · 1820 · 1925 · 2002 · 2275 · 2860 · 3575 · 3850 · 4004 · 4550 · 5005 · 7150 · 7700 · 9100 · 10010 · 14300 · 20020 · 25025 · 50050 (half) · 100100

Aliquot sum (sum of proper divisors): 191,548

Factor pairs (a × b = 100,100)

1 × 100100

2 × 50050

4 × 25025

5 × 20020

7 × 14300

10 × 10010

11 × 9100

13 × 7700

14 × 7150

20 × 5005

22 × 4550

25 × 4004

26 × 3850

28 × 3575

35 × 2860

44 × 2275

50 × 2002

52 × 1925

55 × 1820

65 × 1540

70 × 1430

77 × 1300

91 × 1100

100 × 1001

110 × 910

130 × 770

140 × 715

143 × 700

154 × 650

175 × 572

182 × 550

220 × 455

260 × 385

275 × 364

286 × 350

308 × 325

First multiples

100,100 · 200,200 (double) · 300,300 · 400,400 · 500,500 · 600,600 · 700,700 · 800,800 · 900,900 · 1,001,000

Sums & aliquot sequence

As consecutive integers: 20,018 + 20,019 + 20,020 + 20,021 + 20,022 14,297 + 14,298 + … + 14,303 12,509 + 12,510 + … + 12,516 9,095 + 9,096 + … + 9,105

Aliquot sequence: 100,100 → 191,548 → 191,604 → 319,564 → 331,604 → 383,404 → 383,460 → 971,292 → 1,709,540 → 2,393,692 → 2,487,044 → 2,576,266 → 2,241,974 → 1,601,434 → 1,189,286 → 1,091,674 → 564,506 — unresolved within range

Continued fraction of √n

√100,100 = [316; (2, 1, 1, 2, 4, 2, 4, 9, 1, 1, 1, 24, 1, 1, 1, 9, 4, 2, 4, 2, 1, 1, 2, 632)]

Period length 24 — the block in parentheses repeats forever.

Representations

In words: one hundred thousand one hundred
Ordinal: 100100th
Binary: 11000011100000100
Octal: 303404
Hexadecimal: 0x18704
Base64: AYcE
One's complement: 4,294,867,195 (32-bit)
Scientific notation: 1.001 × 10⁵
As a duration: 100,100 s = 1 day, 3 hours, 48 minutes, 20 seconds

In other bases

ternary (3) 12002022102

quaternary (4) 120130010

quinary (5) 11200400

senary (6) 2051232

septenary (7) 564560

nonary (9) 162272

undecimal (11) 69230

duodecimal (12) 49b18

tridecimal (13) 36740

tetradecimal (14) 286a0

pentadecimal (15) 1e9d5

As an angle

100,100° = 278 × 360° + 20°

20° ≈ 0.349 rad

Compass bearing: NNE (north-northeast)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋
Egyptian hieroglyphic: 𓆐𓍢
Greek (Milesian): ͵ρρʹ
Mayan (base 20): 𝋬·𝋪·𝋥·𝋠
Chinese: 一十萬零一百
Chinese (financial): 壹拾萬零壹佰

In other modern scripts

Eastern Arabic ١٠٠١٠٠ Devanagari १००१०० Bengali ১০০১০০ Tamil ௧௦௦௧௦௦ Thai ๑๐๐๑๐๐ Tibetan ༡༠༠༡༠༠ Khmer ១០០១០០ Lao ໑໐໐໑໐໐ Burmese ၁၀၀၁၀၀

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 100100, here are decompositions:

31 + 100069 = 100100
43 + 100057 = 100100
97 + 100003 = 100100
109 + 99991 = 100100
139 + 99961 = 100100
193 + 99907 = 100100
199 + 99901 = 100100
223 + 99877 = 100100

Showing the first eight; more decompositions exist.

Unicode codepoint

𘜄

Tangut Ideograph-18704

U+18704

Other letter (Lo)

UTF-8 encoding: F0 98 9C 84 (4 bytes).

Lookup U+18704 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#018704

RGB(1, 135, 4)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.1.135.4.

Address: 0.1.135.4
Class: reserved
IPv4-mapped IPv6: ::ffff:0.1.135.4

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 100,100 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 US100,100 on Google Patents ↗ Look up on USPTO ↗

Position in π

The digit sequence 100100 first appears in π at position 334,095 of the decimal expansion (the 334,095ordinal-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 100100 on Pi Search ↗