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137,984

137,984 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.).

137,984 (one hundred thirty-seven thousand nine hundred eighty-four) is an even 6-digit number. It is a composite number with 54 divisors, and factors as 2⁸ × 7² × 11. Its proper divisors sum to 211,540, more than the number itself, making it an abundant number. Written other ways, in hexadecimal, 0x21B00.

Abundant Number Gapful Number Harshad / Niven Odious Number Pernicious Number Practical Number Recamán's Sequence Self Number Semiperfect Number Smith Number

Interestingness

Properties

Parity
Even
Digit count
6
Digit sum
32
Digit product
6,048
Digital root
5
Palindrome
No
Bit width
18 bits
Reversed
489,731
Recamán's sequence
a(492,859) = 137,984
Square (n²)
19,039,584,256
Cube (n³)
2,627,157,993,979,904
Divisor count
54
σ(n) — sum of divisors
349,524
φ(n) — Euler's totient
53,760
Sum of prime factors
41

Primality

Prime factorization: 2 8 × 7 2 × 11

Nearest primes: 137,983 (−1) · 137,993 (+9)

Divisors & multiples

All divisors (54)
1 · 2 · 4 · 7 · 8 · 11 · 14 · 16 · 22 · 28 · 32 · 44 · 49 · 56 · 64 · 77 · 88 · 98 · 112 · 128 · 154 · 176 · 196 · 224 · 256 · 308 · 352 · 392 · 448 · 539 · 616 · 704 · 784 · 896 · 1078 · 1232 · 1408 · 1568 · 1792 · 2156 · 2464 · 2816 · 3136 · 4312 · 4928 · 6272 · 8624 · 9856 · 12544 · 17248 · 19712 · 34496 · 68992 (half) · 137984
Aliquot sum (sum of proper divisors): 211,540
Factor pairs (a × b = 137,984)
1 × 137984
2 × 68992
4 × 34496
7 × 19712
8 × 17248
11 × 12544
14 × 9856
16 × 8624
22 × 6272
28 × 4928
32 × 4312
44 × 3136
49 × 2816
56 × 2464
64 × 2156
77 × 1792
88 × 1568
98 × 1408
112 × 1232
128 × 1078
154 × 896
176 × 784
196 × 704
224 × 616
256 × 539
308 × 448
352 × 392
First multiples
137,984 · 275,968 (double) · 413,952 · 551,936 · 689,920 · 827,904 · 965,888 · 1,103,872 · 1,241,856 · 1,379,840

Sums & aliquot sequence

As consecutive integers: 19,709 + 19,710 + … + 19,715 12,539 + 12,540 + … + 12,549 2,792 + 2,793 + … + 2,840 1,754 + 1,755 + … + 1,830
Aliquot sequence: 137,984 211,540 296,492 296,548 349,832 399,928 349,952 349,096 365,144 372,376 335,024 314,116 300,764 256,660 297,236 250,444 233,396 — unresolved within range

Continued fraction of √n

√137,984 = [371; (2, 6, 13, 2, 1, 4, 1, 2, 1, 28, 1, 45, 2, 6, 1, 14, 3, 2, 1, 1, 2, 1, 3, 1, …)]

Period length 56 — the block in parentheses repeats forever.

Representations

In words
one hundred thirty-seven thousand nine hundred eighty-four
Ordinal
137984th
Binary
100001101100000000
Octal
415400
Hexadecimal
0x21B00
Base64
AhsA
One's complement
4,294,829,311 (32-bit)
Scientific notation
1.37984 × 10⁵
As a duration
137,984 s = 1 day, 14 hours, 19 minutes, 44 seconds
In other bases
ternary (3) 21000021112
quaternary (4) 201230000
quinary (5) 13403414
senary (6) 2542452
septenary (7) 1113200
nonary (9) 230245
undecimal (11) 94740
duodecimal (12) 67a28
tridecimal (13) 4aa62
tetradecimal (14) 38400
pentadecimal (15) 2ad3e
Palindromic in base 6

As an angle

137,984° = 383 × 360° + 104°
104° ≈ 1.815 rad
Compass bearing: ESE (east-southeast)

Historical numeral systems

Babylonian (base 60)
𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒌋𒌋𒁹𒁹𒁹𒁹
Egyptian hieroglyphic
𓆐𓂍𓂍𓂍𓆼𓆼𓆼𓆼𓆼𓆼𓆼𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓎆𓎆𓎆𓎆𓎆𓎆𓎆𓎆𓏺𓏺𓏺𓏺
Greek (Milesian)
͵ρλζϡπδʹ
Mayan (base 20)
𝋱·𝋤·𝋳·𝋤
Chinese
一十三萬七千九百八十四
Chinese (financial)
壹拾參萬柒仟玖佰捌拾肆
In other modern scripts
Eastern Arabic ١٣٧٩٨٤ Devanagari १३७९८४ Bengali ১৩৭৯৮৪ Tamil ௧௩௭௯௮௪ Thai ๑๓๗๙๘๔ Tibetan ༡༣༧༩༨༤ Khmer ១៣៧៩៨៤ Lao ໑໓໗໙໘໔ Burmese ၁၃၇၉၈၄

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 137984, here are decompositions:

  • 37 + 137947 = 137984
  • 43 + 137941 = 137984
  • 73 + 137911 = 137984
  • 157 + 137827 = 137984
  • 181 + 137803 = 137984
  • 193 + 137791 = 137984
  • 241 + 137743 = 137984
  • 271 + 137713 = 137984

Showing the first eight; more decompositions exist.

Unicode codepoint
𡬀
CJK Unified Ideograph-21B00
U+21B00
Other letter (Lo)

UTF-8 encoding: F0 A1 AC 80 (4 bytes).

Hex color
#021B00
RGB(2, 27, 0)
IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.2.27.0.

Address
0.2.27.0
Class
reserved
IPv4-mapped IPv6
::ffff:0.2.27.0

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 137,984 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 137984 first appears in π at position 709,835 of the decimal expansion (the 709,835ordinal-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

  • Mayan numerals — Vigesimal dots-and-bars with a shell zero — one of the earliest true zeros.