Live analysis

472,800

472,800 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.).

472,800 (four hundred seventy-two thousand eight hundred) is an even 6-digit number. It is a composite number with 72 divisors, and factors as 2⁵ × 3 × 5² × 197. Its proper divisors sum to 1,073,976, more than the number itself, making it an abundant number. Written other ways, in hexadecimal, 0x736E0.

Abundant Number Arithmetic Number Evil Number Gapful Number Happy Number Practical Number Weird Number

Interestingness

★ ★ ★ ☆ ☆

5 notable facts · grade C

472,788 472,789 472,790 472,791 472,792 472,793 472,794 472,795 472,796 472,797 472,798 472,799 472,800 472,801 472,802 472,803 472,804 472,805 472,806 472,807 472,808 472,809 472,810 472,811 472,812

less more

Properties

Parity: Even
Digit count: 6
Digit sum: 21
Digit product: 0
Digital root: 3
Palindrome: No
Bit width: 19 bits
Reversed: 8,274
Square (n²): 223,539,840,000
Cube (n³): 105,689,636,352,000,000
Divisor count: 72
σ(n) — sum of divisors: 1,546,776
φ(n) — Euler's totient: 125,440
Sum of prime factors: 220

Primality

Prime factorization: 2 ⁵ × 3 × 5 ² × 197

Nearest primes: 472,799 (−1) · 472,817 (+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 · 197 · 200 · 240 · 300 · 394 · 400 · 480 · 591 · 600 · 788 · 800 · 985 · 1182 · 1200 · 1576 · 1970 · 2364 · 2400 · 2955 · 3152 · 3940 · 4728 · 4925 · 5910 · 6304 · 7880 · 9456 · 9850 · 11820 · 14775 · 15760 · 18912 · 19700 · 23640 · 29550 · 31520 · 39400 · 47280 · 59100 · 78800 · 94560 · 118200 · 157600 · 236400 (half) · 472800

Aliquot sum (sum of proper divisors): 1,073,976

Factor pairs (a × b = 472,800)

1 × 472800

2 × 236400

3 × 157600

4 × 118200

5 × 94560

6 × 78800

8 × 59100

10 × 47280

12 × 39400

15 × 31520

16 × 29550

20 × 23640

24 × 19700

25 × 18912

30 × 15760

32 × 14775

40 × 11820

48 × 9850

50 × 9456

60 × 7880

75 × 6304

80 × 5910

96 × 4925

100 × 4728

120 × 3940

150 × 3152

160 × 2955

197 × 2400

200 × 2364

240 × 1970

300 × 1576

394 × 1200

400 × 1182

480 × 985

591 × 800

600 × 788

First multiples

472,800 · 945,600 (double) · 1,418,400 · 1,891,200 · 2,364,000 · 2,836,800 · 3,309,600 · 3,782,400 · 4,255,200 · 4,728,000

Sums & aliquot sequence

As consecutive integers: 157,599 + 157,600 + 157,601 94,558 + 94,559 + 94,560 + 94,561 + 94,562 31,513 + 31,514 + … + 31,527 18,900 + 18,901 + … + 18,924

Aliquot sequence: 472,800 → 1,073,976 → 1,652,184 → 2,937,816 → 6,854,184 → 12,521,016 → 22,869,144 → 42,126,696 → 76,111,704 → 135,310,296 → 234,786,984 → 358,781,016 → 635,798,184 → 1,223,806,296 → 1,835,709,504 → 3,323,938,800 → 10,022,429,200 — keeps growing

Continued fraction of √n

√472,800 = [687; (1, 1, 1, 1, 8, 4, 1, 1, 1, 3, 1, 7, 2, 1, 5, 13, 1, 1, 2, 1, 3, 1, 2, 2, …)]

Representations

In words: four hundred seventy-two thousand eight hundred
Ordinal: 472800th
Binary: 1110011011011100000
Octal: 1633340
Hexadecimal: 0x736E0
Base64: Bzbg
One's complement: 4,294,494,495 (32-bit)
Scientific notation: 4.728 × 10⁵
As a duration: 472,800 s = 5 days, 11 hours, 20 minutes

In other bases

ternary (3) 220000120010

quaternary (4) 1303123200

quinary (5) 110112200

senary (6) 14044520

septenary (7) 4006266

nonary (9) 800503

undecimal (11) 2a3249

duodecimal (12) 1a9740

tridecimal (13) 137283

tetradecimal (14) c4436

pentadecimal (15) 95150

As an angle

472,800° = 1,313 × 360° + 120°

120° ≈ 2.094 rad

Compass bearing: ESE (east-southeast)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹 𒌋𒁹 𒌋𒌋 ·
Egyptian hieroglyphic: 𓆐𓆐𓆐𓆐𓂍𓂍𓂍𓂍𓂍𓂍𓂍𓆼𓆼𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓍢
Greek (Milesian): ͵υοβωʹ
Chinese: 四十七萬二千八百
Chinese (financial): 肆拾柒萬貳仟捌佰

In other modern scripts

Eastern Arabic ٤٧٢٨٠٠ Devanagari ४७२८०० Bengali ৪৭২৮০০ Tamil ௪௭௨௮௦௦ Thai ๔๗๒๘๐๐ Tibetan ༤༧༢༨༠༠ Khmer ៤៧២៨០០ Lao ໔໗໒໘໐໐ Burmese ၄၇၂၈၀၀

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 472800, here are decompositions:

7 + 472793 = 472800
37 + 472763 = 472800
59 + 472741 = 472800
79 + 472721 = 472800
89 + 472711 = 472800
103 + 472697 = 472800
109 + 472691 = 472800
113 + 472687 = 472800

Showing the first eight; more decompositions exist.

Hex color

#0736E0

RGB(7, 54, 224)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.7.54.224.

Address: 0.7.54.224
Class: reserved
IPv4-mapped IPv6: ::ffff:0.7.54.224

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 472,800 and was likely granted around 1891.

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

Look up US472,800 on Google Patents ↗ Look up on USPTO ↗