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478,800

478,800 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.).

478,800 (four hundred seventy-eight thousand eight hundred) is an even 6-digit number. It is a composite number with 180 divisors, and factors as 2⁴ × 3² × 5² × 7 × 19. Its proper divisors sum to 1,520,080, more than the number itself, making it an abundant number. Written other ways, in hexadecimal, 0x74E50.

Abundant Number Gapful Number Happy Number Odious Number Practical Number Refactorable Number Weird Number

Interestingness

Properties

Parity
Even
Digit count
6
Digit sum
27
Digit product
0
Digital root
9
Palindrome
No
Bit width
19 bits
Reversed
8,874
Square (n²)
229,249,440,000
Cube (n³)
109,764,631,872,000,000
Divisor count
180
σ(n) — sum of divisors
1,998,880
φ(n) — Euler's totient
103,680
Sum of prime factors
50

Primality

Prime factorization: 2 4 × 3 2 × 5 2 × 7 × 19

Nearest primes: 478,787 (−13) · 478,801 (+1)

Divisors & multiples

All divisors (180)
1 · 2 · 3 · 4 · 5 · 6 · 7 · 8 · 9 · 10 · 12 · 14 · 15 · 16 · 18 · 19 · 20 · 21 · 24 · 25 · 28 · 30 · 35 · 36 · 38 · 40 · 42 · 45 · 48 · 50 · 56 · 57 · 60 · 63 · 70 · 72 · 75 · 76 · 80 · 84 · 90 · 95 · 100 · 105 · 112 · 114 · 120 · 126 · 133 · 140 · 144 · 150 · 152 · 168 · 171 · 175 · 180 · 190 · 200 · 210 · 225 · 228 · 240 · 252 · 266 · 280 · 285 · 300 · 304 · 315 · 336 · 342 · 350 · 360 · 380 · 399 · 400 · 420 · 450 · 456 · 475 · 504 · 525 · 532 · 560 · 570 · 600 · 630 · 665 · 684 · 700 · 720 · 760 · 798 · 840 · 855 · 900 · 912 · 950 · 1008 · 1050 · 1064 · 1140 · 1197 · 1200 · 1260 · 1330 · 1368 · 1400 · 1425 · 1520 · 1575 · 1596 · 1680 · 1710 · 1800 · 1900 · 1995 · 2100 · 2128 · 2280 · 2394 · 2520 · 2660 · 2736 · 2800 · 2850 · 3150 · 3192 · 3325 · 3420 · 3600 · 3800 · 3990 · 4200 · 4275 · 4560 · 4788 · 5040 · 5320 · 5700 · 5985 · 6300 · 6384 · 6650 · 6840 · 7600 · 7980 · 8400 · 8550 · 9576 · 9975 · 10640 · 11400 · 11970 · 12600 · 13300 · 13680 · 15960 · 17100 · 19152 · 19950 · 22800 · 23940 · 25200 · 26600 · 29925 · 31920 · 34200 · 39900 · 47880 · 53200 · 59850 · 68400 · 79800 · 95760 · 119700 · 159600 · 239400 (half) · 478800
Aliquot sum (sum of proper divisors): 1,520,080
Factor pairs (a × b = 478,800)
1 × 478800
2 × 239400
3 × 159600
4 × 119700
5 × 95760
6 × 79800
7 × 68400
8 × 59850
9 × 53200
10 × 47880
12 × 39900
14 × 34200
15 × 31920
16 × 29925
18 × 26600
19 × 25200
20 × 23940
21 × 22800
24 × 19950
25 × 19152
28 × 17100
30 × 15960
35 × 13680
36 × 13300
38 × 12600
40 × 11970
42 × 11400
45 × 10640
48 × 9975
50 × 9576
56 × 8550
57 × 8400
60 × 7980
63 × 7600
70 × 6840
72 × 6650
75 × 6384
76 × 6300
80 × 5985
84 × 5700
90 × 5320
95 × 5040
100 × 4788
105 × 4560
112 × 4275
114 × 4200
120 × 3990
126 × 3800
133 × 3600
140 × 3420
144 × 3325
150 × 3192
152 × 3150
168 × 2850
171 × 2800
175 × 2736
180 × 2660
190 × 2520
200 × 2394
210 × 2280
225 × 2128
228 × 2100
240 × 1995
252 × 1900
266 × 1800
280 × 1710
285 × 1680
300 × 1596
304 × 1575
315 × 1520
336 × 1425
342 × 1400
350 × 1368
360 × 1330
380 × 1260
399 × 1200
400 × 1197
420 × 1140
450 × 1064
456 × 1050
475 × 1008
504 × 950
525 × 912
532 × 900
560 × 855
570 × 840
600 × 798
630 × 760
665 × 720
684 × 700
First multiples
478,800 · 957,600 (double) · 1,436,400 · 1,915,200 · 2,394,000 · 2,872,800 · 3,351,600 · 3,830,400 · 4,309,200 · 4,788,000

Sums & aliquot sequence

As consecutive integers: 159,599 + 159,600 + 159,601 95,758 + 95,759 + 95,760 + 95,761 + 95,762 68,397 + 68,398 + … + 68,403 53,196 + 53,197 + … + 53,204
Aliquot sequence: 478,800 1,520,080 2,014,292 2,199,148 2,199,204 4,319,196 7,198,884 16,388,316 30,956,436 65,139,564 109,121,684 109,121,740 172,920,692 172,920,748 254,955,092 280,897,708 324,113,524 — unresolved within range

Continued fraction of √n

√478,800 = [691; (1, 20, 1, 1, 1, 1, 1, 20, 1, 1382)]

Period length 10 — the block in parentheses repeats forever.

Representations

In words
four hundred seventy-eight thousand eight hundred
Ordinal
478800th
Binary
1110100111001010000
Octal
1647120
Hexadecimal
0x74E50
Base64
B05Q
One's complement
4,294,488,495 (32-bit)
Scientific notation
4.788 × 10⁵
As a duration
478,800 s = 5 days, 13 hours
In other bases
ternary (3) 220022210100
quaternary (4) 1310321100
quinary (5) 110310200
senary (6) 14132400
septenary (7) 4032630
nonary (9) 808710
undecimal (11) 2a7803
duodecimal (12) 1b1100
tridecimal (13) 139c1a
tetradecimal (14) c66c0
pentadecimal (15) 96d00

As an angle

478,800° = 1,330 × 360°
0° ≈ 0 rad
Compass bearing: N (north)

Historical numeral systems

Babylonian (base 60)
𒁹𒁹 𒌋𒁹𒁹𒁹 · ·
Egyptian hieroglyphic
𓆐𓆐𓆐𓆐𓂍𓂍𓂍𓂍𓂍𓂍𓂍𓆼𓆼𓆼𓆼𓆼𓆼𓆼𓆼𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓍢
Greek (Milesian)
͵υοηωʹ
Chinese
四十七萬八千八百
Chinese (financial)
肆拾柒萬捌仟捌佰
In other modern scripts
Eastern Arabic ٤٧٨٨٠٠ Devanagari ४७८८०० Bengali ৪৭৮৮০০ Tamil ௪௭௮௮௦௦ Thai ๔๗๘๘๐๐ Tibetan ༤༧༨༨༠༠ Khmer ៤៧៨៨០០ Lao ໔໗໘໘໐໐ Burmese ၄၇၈၈၀၀

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 478800, here are decompositions:

  • 13 + 478787 = 478800
  • 31 + 478769 = 478800
  • 37 + 478763 = 478800
  • 53 + 478747 = 478800
  • 59 + 478741 = 478800
  • 61 + 478739 = 478800
  • 71 + 478729 = 478800
  • 73 + 478727 = 478800

Showing the first eight; more decompositions exist.

Hex color
#074E50
RGB(7, 78, 80)
IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.7.78.80.

Address
0.7.78.80
Class
reserved
IPv4-mapped IPv6
::ffff:0.7.78.80

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 478,800 and was likely granted around 1892.

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

Position in π

The digit sequence 478800 first appears in π at position 461,489 of the decimal expansion (the 461,489ordinal-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°.