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138,624

138,624 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.).

138,624 (one hundred thirty-eight thousand six hundred twenty-four) is an even 6-digit number. It is a composite number with 48 divisors, and factors as 2⁷ × 3 × 19². Its proper divisors sum to 249,996, more than the number itself, making it an abundant number. Written other ways, in hexadecimal, 0x21D80.

Abundant Number Evil Number Happy Number Harshad / Niven Practical Number Recamán's Sequence Refactorable Number Semiperfect Number

Interestingness

Properties

Parity
Even
Digit count
6
Digit sum
24
Digit product
1,152
Digital root
6
Palindrome
No
Bit width
18 bits
Reversed
426,831
Recamán's sequence
a(491,579) = 138,624
Square (n²)
19,216,613,376
Cube (n³)
2,663,883,812,634,624
Divisor count
48
σ(n) — sum of divisors
388,620
φ(n) — Euler's totient
43,776
Sum of prime factors
55

Primality

Prime factorization: 2 7 × 3 × 19 2

Nearest primes: 138,617 (−7) · 138,629 (+5)

Divisors & multiples

All divisors (48)
1 · 2 · 3 · 4 · 6 · 8 · 12 · 16 · 19 · 24 · 32 · 38 · 48 · 57 · 64 · 76 · 96 · 114 · 128 · 152 · 192 · 228 · 304 · 361 · 384 · 456 · 608 · 722 · 912 · 1083 · 1216 · 1444 · 1824 · 2166 · 2432 · 2888 · 3648 · 4332 · 5776 · 7296 · 8664 · 11552 · 17328 · 23104 · 34656 · 46208 · 69312 (half) · 138624
Aliquot sum (sum of proper divisors): 249,996
Factor pairs (a × b = 138,624)
1 × 138624
2 × 69312
3 × 46208
4 × 34656
6 × 23104
8 × 17328
12 × 11552
16 × 8664
19 × 7296
24 × 5776
32 × 4332
38 × 3648
48 × 2888
57 × 2432
64 × 2166
76 × 1824
96 × 1444
114 × 1216
128 × 1083
152 × 912
192 × 722
228 × 608
304 × 456
361 × 384
First multiples
138,624 · 277,248 (double) · 415,872 · 554,496 · 693,120 · 831,744 · 970,368 · 1,108,992 · 1,247,616 · 1,386,240

Sums & aliquot sequence

As consecutive integers: 46,207 + 46,208 + 46,209 7,287 + 7,288 + … + 7,305 2,404 + 2,405 + … + 2,460 414 + 415 + … + 669
Aliquot sequence: 138,624 249,996 342,708 456,972 621,924 829,260 1,843,956 3,345,228 5,311,420 5,842,604 4,381,960 6,867,320 9,494,680 15,528,920 23,934,280 33,089,720 41,754,280 — unresolved within range

Continued fraction of √n

√138,624 = [372; (3, 9, 1, 6, 1, 1, 5, 3, 1, 1, 9, 1, 11, 1, 1, 46, 49, 1, 1, 1, 1, 1, 3, 1, …)]

Representations

In words
one hundred thirty-eight thousand six hundred twenty-four
Ordinal
138624th
Binary
100001110110000000
Octal
416600
Hexadecimal
0x21D80
Base64
Ah2A
One's complement
4,294,828,671 (32-bit)
Scientific notation
1.38624 × 10⁵
As a duration
138,624 s = 1 day, 14 hours, 30 minutes, 24 seconds
In other bases
ternary (3) 21001011020
quaternary (4) 201312000
quinary (5) 13413444
senary (6) 2545440
septenary (7) 1115103
nonary (9) 231136
undecimal (11) 95172
duodecimal (12) 68280
tridecimal (13) 4b135
tetradecimal (14) 3873a
pentadecimal (15) 2b119

As an angle

138,624° = 385 × 360° + 24°
24° ≈ 0.419 rad
Compass bearing: NNE (north-northeast)

Historical numeral systems

Babylonian (base 60)
𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒌋 𒌋𒌋𒁹𒁹𒁹𒁹
Egyptian hieroglyphic
𓆐𓂍𓂍𓂍𓆼𓆼𓆼𓆼𓆼𓆼𓆼𓆼𓍢𓍢𓍢𓍢𓍢𓍢𓎆𓎆𓏺𓏺𓏺𓏺
Greek (Milesian)
͵ρληχκδʹ
Mayan (base 20)
𝋱·𝋦·𝋫·𝋤
Chinese
一十三萬八千六百二十四
Chinese (financial)
壹拾參萬捌仟陸佰貳拾肆
In other modern scripts
Eastern Arabic ١٣٨٦٢٤ Devanagari १३८६२४ Bengali ১৩৮৬২৪ Tamil ௧௩௮௬௨௪ Thai ๑๓๘๖๒๔ Tibetan ༡༣༨༦༢༤ Khmer ១៣៨៦២៤ Lao ໑໓໘໖໒໔ Burmese ၁၃၈၆၂၄

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 138624, here are decompositions:

  • 7 + 138617 = 138624
  • 37 + 138587 = 138624
  • 43 + 138581 = 138624
  • 47 + 138577 = 138624
  • 53 + 138571 = 138624
  • 61 + 138563 = 138624
  • 107 + 138517 = 138624
  • 113 + 138511 = 138624

Showing the first eight; more decompositions exist.

Unicode codepoint
𡶀
CJK Unified Ideograph-21D80
U+21D80
Other letter (Lo)

UTF-8 encoding: F0 A1 B6 80 (4 bytes).

Hex color
#021D80
RGB(2, 29, 128)
IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.2.29.128.

Address
0.2.29.128
Class
reserved
IPv4-mapped IPv6
::ffff:0.2.29.128

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 138,624 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 138624 first appears in π at position 671,309 of the decimal expansion (the 671,309ordinal-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°.