Live analysis

137,040

137,040 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.).

137,040 (one hundred thirty-seven thousand forty) is an even 6-digit number. It is a composite number with 40 divisors, and factors as 2⁴ × 3 × 5 × 571. Its proper divisors sum to 288,528, more than the number itself, making it an abundant number. Written other ways, in hexadecimal, 0x21750.

Abundant Number Gapful Number Harshad / Niven Odious Number Pernicious Number Practical Number Refactorable Number Semiperfect Number

Interestingness

★ ★ ★ ☆ ☆

5 notable facts · grade C

137,028 137,029 137,030 137,031 137,032 137,033 137,034 137,035 137,036 137,037 137,038 137,039 137,040 137,041 137,042 137,043 137,044 137,045 137,046 137,047 137,048 137,049 137,050 137,051 137,052

less more

Properties

Parity: Even
Digit count: 6
Digit sum: 15
Digit product: 0
Digital root: 6
Palindrome: No
Bit width: 18 bits
Reversed: 40,731
Square (n²): 18,779,961,600
Cube (n³): 2,573,605,937,664,000
Divisor count: 40
σ(n) — sum of divisors: 425,568
φ(n) — Euler's totient: 36,480
Sum of prime factors: 587

Primality

Prime factorization: 2 ⁴ × 3 × 5 × 571

Nearest primes: 137,029 (−11) · 137,077 (+37)

Divisors & multiples

All divisors (40)

1 · 2 · 3 · 4 · 5 · 6 · 8 · 10 · 12 · 15 · 16 · 20 · 24 · 30 · 40 · 48 · 60 · 80 · 120 · 240 · 571 · 1142 · 1713 · 2284 · 2855 · 3426 · 4568 · 5710 · 6852 · 8565 · 9136 · 11420 · 13704 · 17130 · 22840 · 27408 · 34260 · 45680 · 68520 (half) · 137040

Aliquot sum (sum of proper divisors): 288,528

Factor pairs (a × b = 137,040)

1 × 137040

2 × 68520

3 × 45680

4 × 34260

5 × 27408

6 × 22840

8 × 17130

10 × 13704

12 × 11420

15 × 9136

16 × 8565

20 × 6852

24 × 5710

30 × 4568

40 × 3426

48 × 2855

60 × 2284

80 × 1713

120 × 1142

240 × 571

First multiples

137,040 · 274,080 (double) · 411,120 · 548,160 · 685,200 · 822,240 · 959,280 · 1,096,320 · 1,233,360 · 1,370,400

Sums & aliquot sequence

As consecutive integers: 45,679 + 45,680 + 45,681 27,406 + 27,407 + 27,408 + 27,409 + 27,410 9,129 + 9,130 + … + 9,143 4,267 + 4,268 + … + 4,298

Aliquot sequence: 137,040 → 288,528 → 456,960 → 1,309,056 → 2,673,024 → 4,428,216 → 9,683,784 → 18,929,736 → 43,183,224 → 93,397,896 → 159,554,934 → 286,220,682 → 419,494,518 → 518,454,282 → 520,854,198 → 521,382,522 → 522,940,038 — unresolved within range

Continued fraction of √n

√137,040 = [370; (5, 3, 2, 14, 1, 2, 10, 11, 2, 8, 2, 1, 48, 1, 2, 8, 2, 11, 10, 2, 1, 14, 2, 3, …)]

Period length 26 — the block in parentheses repeats forever.

Representations

In words: one hundred thirty-seven thousand forty
Ordinal: 137040th
Binary: 100001011101010000
Octal: 413520
Hexadecimal: 0x21750
Base64: AhdQ
One's complement: 4,294,830,255 (32-bit)
Scientific notation: 1.3704 × 10⁵
As a duration: 137,040 s = 1 day, 14 hours, 4 minutes

In other bases

ternary (3) 20221222120

quaternary (4) 201131100

quinary (5) 13341130

senary (6) 2534240

septenary (7) 1110351

nonary (9) 227876

undecimal (11) 93a62

duodecimal (12) 67380

tridecimal (13) 4a4b7

tetradecimal (14) 37d28

pentadecimal (15) 2a910

As an angle

137,040° = 380 × 360° + 240°

240° ≈ 4.189 rad

Compass bearing: WSW (west-southwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒁹𒁹𒁹𒁹 ·
Egyptian hieroglyphic: 𓆐𓂍𓂍𓂍𓆼𓆼𓆼𓆼𓆼𓆼𓆼𓎆𓎆𓎆𓎆
Greek (Milesian): ͵ρλζμʹ
Mayan (base 20): 𝋱·𝋢·𝋬·𝋠
Chinese: 一十三萬七千零四十
Chinese (financial): 壹拾參萬柒仟零肆拾

In other modern scripts

Eastern Arabic ١٣٧٠٤٠ Devanagari १३७०४० Bengali ১৩৭০৪০ Tamil ௧௩௭௦௪௦ Thai ๑๓๗๐๔๐ Tibetan ༡༣༧༠༤༠ Khmer ១៣៧០៤០ Lao ໑໓໗໐໔໐ Burmese ၁၃၇၀၄၀

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 137040, here are decompositions:

11 + 137029 = 137040
41 + 136999 = 137040
47 + 136993 = 137040
53 + 136987 = 137040
61 + 136979 = 137040
67 + 136973 = 137040
89 + 136951 = 137040
97 + 136943 = 137040

Showing the first eight; more decompositions exist.

Unicode codepoint

𡝐

CJK Unified Ideograph-21750

U+21750

Other letter (Lo)

UTF-8 encoding: F0 A1 9D 90 (4 bytes).

Lookup U+21750 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#021750

RGB(2, 23, 80)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.2.23.80.

Address: 0.2.23.80
Class: reserved
IPv4-mapped IPv6: ::ffff:0.2.23.80

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 137,040 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 US137,040 on Google Patents ↗ Look up on USPTO ↗