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506,400

506,400 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.).

506,400 (five hundred six thousand four hundred) is an even 6-digit number. It is a composite number with 72 divisors, and factors as 2⁵ × 3 × 5² × 211. Its proper divisors sum to 1,149,744, more than the number itself, making it an abundant number. Written other ways, in hexadecimal, 0x7BA20.

Abundant Number Arithmetic Number Gapful Number Harshad / Niven Odious Number Practical Number Self Number Weird Number

Interestingness

Properties

Parity
Even
Digit count
6
Digit sum
15
Digit product
0
Digital root
6
Palindrome
No
Bit width
19 bits
Reversed
4,605
Square (n²)
256,440,960,000
Cube (n³)
129,861,702,144,000,000
Divisor count
72
σ(n) — sum of divisors
1,656,144
φ(n) — Euler's totient
134,400
Sum of prime factors
234

Primality

Prime factorization: 2 5 × 3 × 5 2 × 211

Nearest primes: 506,393 (−7) · 506,417 (+17)

Divisors & multiples

All divisors (72)
1 · 2 · 3 · 4 · 5 · 6 · 8 · 10 · 12 · 15 · 16 · 20 · 24 · 25 · 30 · 32 · 40 · 48 · 50 · 60 · 75 · 80 · 96 · 100 · 120 · 150 · 160 · 200 · 211 · 240 · 300 · 400 · 422 · 480 · 600 · 633 · 800 · 844 · 1055 · 1200 · 1266 · 1688 · 2110 · 2400 · 2532 · 3165 · 3376 · 4220 · 5064 · 5275 · 6330 · 6752 · 8440 · 10128 · 10550 · 12660 · 15825 · 16880 · 20256 · 21100 · 25320 · 31650 · 33760 · 42200 · 50640 · 63300 · 84400 · 101280 · 126600 · 168800 · 253200 (half) · 506400
Aliquot sum (sum of proper divisors): 1,149,744
Factor pairs (a × b = 506,400)
1 × 506400
2 × 253200
3 × 168800
4 × 126600
5 × 101280
6 × 84400
8 × 63300
10 × 50640
12 × 42200
15 × 33760
16 × 31650
20 × 25320
24 × 21100
25 × 20256
30 × 16880
32 × 15825
40 × 12660
48 × 10550
50 × 10128
60 × 8440
75 × 6752
80 × 6330
96 × 5275
100 × 5064
120 × 4220
150 × 3376
160 × 3165
200 × 2532
211 × 2400
240 × 2110
300 × 1688
400 × 1266
422 × 1200
480 × 1055
600 × 844
633 × 800
First multiples
506,400 · 1,012,800 (double) · 1,519,200 · 2,025,600 · 2,532,000 · 3,038,400 · 3,544,800 · 4,051,200 · 4,557,600 · 5,064,000

Sums & aliquot sequence

As consecutive integers: 168,799 + 168,800 + 168,801 101,278 + 101,279 + 101,280 + 101,281 + 101,282 33,753 + 33,754 + … + 33,767 20,244 + 20,245 + … + 20,268
Aliquot sequence: 506,400 1,149,744 1,997,376 3,391,488 6,831,816 10,247,784 15,758,136 28,397,664 53,017,488 95,849,100 206,449,260 401,979,540 725,956,332 1,100,606,868 1,681,482,806 840,922,618 420,461,312 — unresolved within range

Continued fraction of √n

√506,400 = [711; (1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 1, 1, 1, 2, 3, 2, 2, 1, 1, 6, 2, 56, 2, 6, …)]

Period length 44 — the block in parentheses repeats forever.

Representations

In words
five hundred six thousand four hundred
Ordinal
506400th
Binary
1111011101000100000
Octal
1735040
Hexadecimal
0x7BA20
Base64
B7og
One's complement
4,294,460,895 (32-bit)
Scientific notation
5.064 × 10⁵
As a duration
506,400 s = 5 days, 20 hours, 40 minutes
In other bases
ternary (3) 221201122120
quaternary (4) 1323220200
quinary (5) 112201100
senary (6) 14504240
septenary (7) 4206246
nonary (9) 851576
undecimal (11) 316514
duodecimal (12) 205080
tridecimal (13) 14965b
tetradecimal (14) d2796
pentadecimal (15) a00a0

As an angle

506,400° = 1,406 × 360° + 240°
240° ≈ 4.189 rad
Compass bearing: WSW (west-southwest)

Historical numeral systems

Babylonian (base 60)
𒁹𒁹 𒌋𒌋 𒌋𒌋𒌋𒌋 ·
Egyptian hieroglyphic
𓆐𓆐𓆐𓆐𓆐𓆼𓆼𓆼𓆼𓆼𓆼𓍢𓍢𓍢𓍢
Greek (Milesian)
͵φϛυʹ
Chinese
五十萬六千四百
Chinese (financial)
伍拾萬陸仟肆佰
In other modern scripts
Eastern Arabic ٥٠٦٤٠٠ Devanagari ५०६४०० Bengali ৫০৬৪০০ Tamil ௫௦௬௪௦௦ Thai ๕๐๖๔๐๐ Tibetan ༥༠༦༤༠༠ Khmer ៥០៦៤០០ Lao ໕໐໖໔໐໐ Burmese ၅၀၆၄၀၀

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 506400, here are decompositions:

  • 7 + 506393 = 506400
  • 19 + 506381 = 506400
  • 43 + 506357 = 506400
  • 53 + 506347 = 506400
  • 61 + 506339 = 506400
  • 67 + 506333 = 506400
  • 71 + 506329 = 506400
  • 73 + 506327 = 506400

Showing the first eight; more decompositions exist.

Hex color
#07BA20
RGB(7, 186, 32)
IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.7.186.32.

Address
0.7.186.32
Class
reserved
IPv4-mapped IPv6
::ffff:0.7.186.32

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 506,400 and was likely granted around 1893.

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

Related reading

  • Babylonian numerals — The base-60 cuneiform system that gave us 60 minutes, 60 seconds, and 360°.