Live analysis

137,100

137,100 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.).

137,100 (one hundred thirty-seven thousand one hundred) is an even 6-digit number. It is a composite number with 36 divisors, and factors as 2² × 3 × 5² × 457. Its proper divisors sum to 260,444, more than the number itself, making it an abundant number. Written other ways, in hexadecimal, 0x2178C.

Abundant Number Cube-Free Evil Number Gapful Number Harshad / Niven Practical Number Semiperfect Number

Interestingness

★ ★ ★ ☆ ☆

5 notable facts · grade C

137,088 137,089 137,090 137,091 137,092 137,093 137,094 137,095 137,096 137,097 137,098 137,099 137,100 137,101 137,102 137,103 137,104 137,105 137,106 137,107 137,108 137,109 137,110 137,111 137,112

less more

Properties

Parity: Even
Digit count: 6
Digit sum: 12
Digit product: 0
Digital root: 3
Palindrome: No
Bit width: 18 bits
Reversed: 1,731
Square (n²): 18,796,410,000
Cube (n³): 2,576,987,811,000,000
Divisor count: 36
σ(n) — sum of divisors: 397,544
φ(n) — Euler's totient: 36,480
Sum of prime factors: 474

Primality

Prime factorization: 2 ² × 3 × 5 ² × 457

Nearest primes: 137,089 (−11) · 137,117 (+17)

Divisors & multiples

All divisors (36)

1 · 2 · 3 · 4 · 5 · 6 · 10 · 12 · 15 · 20 · 25 · 30 · 50 · 60 · 75 · 100 · 150 · 300 · 457 · 914 · 1371 · 1828 · 2285 · 2742 · 4570 · 5484 · 6855 · 9140 · 11425 · 13710 · 22850 · 27420 · 34275 · 45700 · 68550 (half) · 137100

Aliquot sum (sum of proper divisors): 260,444

Factor pairs (a × b = 137,100)

1 × 137100

2 × 68550

3 × 45700

4 × 34275

5 × 27420

6 × 22850

10 × 13710

12 × 11425

15 × 9140

20 × 6855

25 × 5484

30 × 4570

50 × 2742

60 × 2285

75 × 1828

100 × 1371

150 × 914

300 × 457

First multiples

137,100 · 274,200 (double) · 411,300 · 548,400 · 685,500 · 822,600 · 959,700 · 1,096,800 · 1,233,900 · 1,371,000

Sums & aliquot sequence

As consecutive integers: 45,699 + 45,700 + 45,701 27,418 + 27,419 + 27,420 + 27,421 + 27,422 17,134 + 17,135 + … + 17,141 9,133 + 9,134 + … + 9,147

Aliquot sequence: 137,100 → 260,444 → 195,340 → 214,916 → 190,216 → 212,984 → 192,616 → 168,554 → 88,054 → 44,030 → 54,466 → 28,298 → 14,152 → 13,748 → 13,804 → 16,436 → 16,492 — unresolved within range

Continued fraction of √n

√137,100 = [370; (3, 1, 2, 2, 1, 6, 1, 2, 2, 1, 3, 740)]

Period length 12 — the block in parentheses repeats forever.

Representations

In words: one hundred thirty-seven thousand one hundred
Ordinal: 137100th
Binary: 100001011110001100
Octal: 413614
Hexadecimal: 0x2178C
Base64: AheM
One's complement: 4,294,830,195 (32-bit)
Scientific notation: 1.371 × 10⁵
As a duration: 137,100 s = 1 day, 14 hours, 5 minutes

In other bases

ternary (3) 20222001210

quaternary (4) 201132030

quinary (5) 13341400

senary (6) 2534420

septenary (7) 1110465

nonary (9) 228053

undecimal (11) 94007

duodecimal (12) 67410

tridecimal (13) 4a532

tetradecimal (14) 37d6c

pentadecimal (15) 2a950

As an angle

137,100° = 380 × 360° + 300°

300° ≈ 5.236 rad

Compass bearing: WNW (west-northwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒁹𒁹𒁹𒁹𒁹 ·
Egyptian hieroglyphic: 𓆐𓂍𓂍𓂍𓆼𓆼𓆼𓆼𓆼𓆼𓆼𓍢
Greek (Milesian): ͵ρλζρʹ
Mayan (base 20): 𝋱·𝋢·𝋯·𝋠
Chinese: 一十三萬七千一百
Chinese (financial): 壹拾參萬柒仟壹佰

In other modern scripts

Eastern Arabic ١٣٧١٠٠ Devanagari १३७१०० Bengali ১৩৭১০০ Tamil ௧௩௭௧௦௦ Thai ๑๓๗๑๐๐ Tibetan ༡༣༧༡༠༠ Khmer ១៣៧១០០ Lao ໑໓໗໑໐໐ Burmese ၁၃၇၁၀၀

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 137100, here are decompositions:

11 + 137089 = 137100
13 + 137087 = 137100
23 + 137077 = 137100
71 + 137029 = 137100
101 + 136999 = 137100
107 + 136993 = 137100
109 + 136991 = 137100
113 + 136987 = 137100

Showing the first eight; more decompositions exist.

Unicode codepoint

𡞌

CJK Unified Ideograph-2178C

U+2178C

Other letter (Lo)

UTF-8 encoding: F0 A1 9E 8C (4 bytes).

Lookup U+2178C on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#02178C

RGB(2, 23, 140)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.2.23.140.

Address: 0.2.23.140
Class: reserved
IPv4-mapped IPv6: ::ffff:0.2.23.140

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 137,100 and was likely granted around 1872.

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

Look up US137,100 on Google Patents ↗ Look up on USPTO ↗

Position in π

The digit sequence 137100 first appears in π at position 140,971 of the decimal expansion (the 140,971ordinal-suffix:st 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 137100 on Pi Search ↗