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137,760

137,760 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.).

137,760 (one hundred thirty-seven thousand seven hundred sixty) is an even 6-digit number. It is a composite number with 96 divisors, and factors as 2⁵ × 3 × 5 × 7 × 41. Its proper divisors sum to 370,272, more than the number itself, making it an abundant number. Written other ways, in hexadecimal, 0x21A20.

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

Interestingness

Properties

Parity
Even
Digit count
6
Digit sum
24
Digit product
0
Digital root
6
Palindrome
No
Bit width
18 bits
Reversed
67,731
Recamán's sequence
a(493,307) = 137,760
Square (n²)
18,977,817,600
Cube (n³)
2,614,384,152,576,000
Divisor count
96
σ(n) — sum of divisors
508,032
φ(n) — Euler's totient
30,720
Sum of prime factors
66

Primality

Prime factorization: 2 5 × 3 × 5 × 7 × 41

Nearest primes: 137,743 (−17) · 137,771 (+11)

Divisors & multiples

All divisors (96)
1 · 2 · 3 · 4 · 5 · 6 · 7 · 8 · 10 · 12 · 14 · 15 · 16 · 20 · 21 · 24 · 28 · 30 · 32 · 35 · 40 · 41 · 42 · 48 · 56 · 60 · 70 · 80 · 82 · 84 · 96 · 105 · 112 · 120 · 123 · 140 · 160 · 164 · 168 · 205 · 210 · 224 · 240 · 246 · 280 · 287 · 328 · 336 · 410 · 420 · 480 · 492 · 560 · 574 · 615 · 656 · 672 · 820 · 840 · 861 · 984 · 1120 · 1148 · 1230 · 1312 · 1435 · 1640 · 1680 · 1722 · 1968 · 2296 · 2460 · 2870 · 3280 · 3360 · 3444 · 3936 · 4305 · 4592 · 4920 · 5740 · 6560 · 6888 · 8610 · 9184 · 9840 · 11480 · 13776 · 17220 · 19680 · 22960 · 27552 · 34440 · 45920 · 68880 (half) · 137760
Aliquot sum (sum of proper divisors): 370,272
Factor pairs (a × b = 137,760)
1 × 137760
2 × 68880
3 × 45920
4 × 34440
5 × 27552
6 × 22960
7 × 19680
8 × 17220
10 × 13776
12 × 11480
14 × 9840
15 × 9184
16 × 8610
20 × 6888
21 × 6560
24 × 5740
28 × 4920
30 × 4592
32 × 4305
35 × 3936
40 × 3444
41 × 3360
42 × 3280
48 × 2870
56 × 2460
60 × 2296
70 × 1968
80 × 1722
82 × 1680
84 × 1640
96 × 1435
105 × 1312
112 × 1230
120 × 1148
123 × 1120
140 × 984
160 × 861
164 × 840
168 × 820
205 × 672
210 × 656
224 × 615
240 × 574
246 × 560
280 × 492
287 × 480
328 × 420
336 × 410
First multiples
137,760 · 275,520 (double) · 413,280 · 551,040 · 688,800 · 826,560 · 964,320 · 1,102,080 · 1,239,840 · 1,377,600

Sums & aliquot sequence

As consecutive integers: 45,919 + 45,920 + 45,921 27,550 + 27,551 + 27,552 + 27,553 + 27,554 19,677 + 19,678 + … + 19,683 9,177 + 9,178 + … + 9,191
Aliquot sequence: 137,760 370,272 839,328 1,680,672 3,568,992 7,462,560 19,414,752 39,516,960 110,473,440 339,497,760 899,132,640 2,384,205,600 6,485,101,728 13,163,035,872 — keeps growing

Continued fraction of √n

√137,760 = [371; (6, 4, 4, 2, 3, 185, 3, 2, 4, 4, 6, 742)]

Period length 12 — the block in parentheses repeats forever.

Representations

In words
one hundred thirty-seven thousand seven hundred sixty
Ordinal
137760th
Binary
100001101000100000
Octal
415040
Hexadecimal
0x21A20
Base64
Ahog
One's complement
4,294,829,535 (32-bit)
Scientific notation
1.3776 × 10⁵
As a duration
137,760 s = 1 day, 14 hours, 16 minutes
In other bases
ternary (3) 20222222020
quaternary (4) 201220200
quinary (5) 13402020
senary (6) 2541440
septenary (7) 1112430
nonary (9) 228866
undecimal (11) 94557
duodecimal (12) 67880
tridecimal (13) 4a91c
tetradecimal (14) 382c0
pentadecimal (15) 2ac40

As an angle

137,760° = 382 × 360° + 240°
240° ≈ 4.189 rad
Compass bearing: WSW (west-southwest)

Historical numeral systems

Babylonian (base 60)
𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒁹𒁹𒁹𒁹𒁹𒁹 ·
Egyptian hieroglyphic
𓆐𓂍𓂍𓂍𓆼𓆼𓆼𓆼𓆼𓆼𓆼𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓎆𓎆𓎆𓎆𓎆𓎆
Greek (Milesian)
͵ρλζψξʹ
Mayan (base 20)
𝋱·𝋤·𝋨·𝋠
Chinese
一十三萬七千七百六十
Chinese (financial)
壹拾參萬柒仟柒佰陸拾
In other modern scripts
Eastern Arabic ١٣٧٧٦٠ Devanagari १३७७६० Bengali ১৩৭৭৬০ Tamil ௧௩௭௭௬௦ Thai ๑๓๗๗๖๐ Tibetan ༡༣༧༧༦༠ Khmer ១៣៧៧៦០ Lao ໑໓໗໗໖໐ Burmese ၁၃၇၇၆၀

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 137760, here are decompositions:

  • 17 + 137743 = 137760
  • 23 + 137737 = 137760
  • 37 + 137723 = 137760
  • 47 + 137713 = 137760
  • 53 + 137707 = 137760
  • 61 + 137699 = 137760
  • 101 + 137659 = 137760
  • 107 + 137653 = 137760

Showing the first eight; more decompositions exist.

Unicode codepoint
𡨠
CJK Unified Ideograph-21A20
U+21A20
Other letter (Lo)

UTF-8 encoding: F0 A1 A8 A0 (4 bytes).

Hex color
#021A20
RGB(2, 26, 32)
IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.2.26.32.

Address
0.2.26.32
Class
reserved
IPv4-mapped IPv6
::ffff:0.2.26.32

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 137,760 and was likely granted around 1872.

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

Position in π

The digit sequence 137760 first appears in π at position 447,960 of the decimal expansion (the 447,960ordinal-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°.