Live analysis

513,072

513,072 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.).

513,072 (five hundred thirteen thousand seventy-two) is an even 6-digit number. It is a composite number with 60 divisors, and factors as 2⁴ × 3² × 7 × 509. Its proper divisors sum to 1,131,168, more than the number itself, making it an abundant number. Written other ways, in hexadecimal, 0x7D430.

Abundant Number Arithmetic Number Harshad / Niven Odious Number Practical Number Semiperfect Number

Interestingness

★ ★ ☆ ☆ ☆

4 notable facts · grade D

513,060 513,061 513,062 513,063 513,064 513,065 513,066 513,067 513,068 513,069 513,070 513,071 513,072 513,073 513,074 513,075 513,076 513,077 513,078 513,079 513,080 513,081 513,082 513,083 513,084

less more

Properties

Parity: Even
Digit count: 6
Digit sum: 18
Digit product: 0
Digital root: 9
Palindrome: No
Bit width: 19 bits
Reversed: 270,315
Square (n²): 263,242,877,184
Cube (n³): 135,062,549,482,549,248
Divisor count: 60
σ(n) — sum of divisors: 1,644,240
φ(n) — Euler's totient: 146,304
Sum of prime factors: 530

Primality

Prime factorization: 2 ⁴ × 3 ² × 7 × 509

Nearest primes: 513,067 (−5) · 513,083 (+11)

Divisors & multiples

All divisors (60)

1 · 2 · 3 · 4 · 6 · 7 · 8 · 9 · 12 · 14 · 16 · 18 · 21 · 24 · 28 · 36 · 42 · 48 · 56 · 63 · 72 · 84 · 112 · 126 · 144 · 168 · 252 · 336 · 504 · 509 · 1008 · 1018 · 1527 · 2036 · 3054 · 3563 · 4072 · 4581 · 6108 · 7126 · 8144 · 9162 · 10689 · 12216 · 14252 · 18324 · 21378 · 24432 · 28504 · 32067 · 36648 · 42756 · 57008 · 64134 · 73296 · 85512 · 128268 · 171024 · 256536 (half) · 513072

Aliquot sum (sum of proper divisors): 1,131,168

Factor pairs (a × b = 513,072)

1 × 513072

2 × 256536

3 × 171024

4 × 128268

6 × 85512

7 × 73296

8 × 64134

9 × 57008

12 × 42756

14 × 36648

16 × 32067

18 × 28504

21 × 24432

24 × 21378

28 × 18324

36 × 14252

42 × 12216

48 × 10689

56 × 9162

63 × 8144

72 × 7126

84 × 6108

112 × 4581

126 × 4072

144 × 3563

168 × 3054

252 × 2036

336 × 1527

504 × 1018

509 × 1008

First multiples

513,072 · 1,026,144 (double) · 1,539,216 · 2,052,288 · 2,565,360 · 3,078,432 · 3,591,504 · 4,104,576 · 4,617,648 · 5,130,720

Sums & aliquot sequence

As consecutive integers: 171,023 + 171,024 + 171,025 73,293 + 73,294 + … + 73,299 57,004 + 57,005 + … + 57,012 24,422 + 24,423 + … + 24,442

Aliquot sequence: 513,072 → 1,131,168 → 1,838,400 → 4,208,832 → 7,856,676 → 13,240,764 → 20,416,860 → 43,823,316 → 58,431,116 → 43,823,344 → 41,187,336 → 61,781,064 → 92,671,656 → 196,180,824 → 393,297,576 → 730,410,264 → 1,399,176,936 — unresolved within range

Continued fraction of √n

√513,072 = [716; (3, 2, 3, 1, 7, 1, 4, 9, 2, 9, 2, 9, 4, 1, 7, 1, 3, 2, 3, 1432)]

Period length 20 — the block in parentheses repeats forever.

Representations

In words: five hundred thirteen thousand seventy-two
Ordinal: 513072nd
Binary: 1111101010000110000
Octal: 1752060
Hexadecimal: 0x7D430
Base64: B9Qw
One's complement: 4,294,454,223 (32-bit)
Scientific notation: 5.13072 × 10⁵
As a duration: 513,072 s = 5 days, 22 hours, 31 minutes, 12 seconds

In other bases

ternary (3) 222001210200

quaternary (4) 1331100300

quinary (5) 112404242

senary (6) 14555200

septenary (7) 4234560

nonary (9) 861720

undecimal (11) 32052a

duodecimal (12) 208b00

tridecimal (13) 14c6c1

tetradecimal (14) d4da0

pentadecimal (15) a204c

As an angle

513,072° = 1,425 × 360° + 72°

72° ≈ 1.257 rad

Compass bearing: ENE (east-northeast)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹 𒌋𒌋𒁹𒁹 𒌋𒌋𒌋𒁹 𒌋𒁹𒁹
Egyptian hieroglyphic: 𓆐𓆐𓆐𓆐𓆐𓂍𓆼𓆼𓆼𓎆𓎆𓎆𓎆𓎆𓎆𓎆𓏺𓏺
Greek (Milesian): ͵φιγοβʹ
Chinese: 五十一萬三千零七十二
Chinese (financial): 伍拾壹萬參仟零柒拾貳

In other modern scripts

Eastern Arabic ٥١٣٠٧٢ Devanagari ५१३०७२ Bengali ৫১৩০৭২ Tamil ௫௧௩௦௭௨ Thai ๕๑๓๐๗๒ Tibetan ༥༡༣༠༧༢ Khmer ៥១៣០៧២ Lao ໕໑໓໐໗໒ Burmese ၅၁၃၀၇၂

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 513072, here are decompositions:

5 + 513067 = 513072
13 + 513059 = 513072
19 + 513053 = 513072
31 + 513041 = 513072
41 + 513031 = 513072
59 + 513013 = 513072
71 + 513001 = 513072
73 + 512999 = 513072

Showing the first eight; more decompositions exist.

Hex color

#07D430

RGB(7, 212, 48)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.7.212.48.

Address: 0.7.212.48
Class: reserved
IPv4-mapped IPv6: ::ffff:0.7.212.48

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 513,072 and was likely granted around 1893.

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

Look up US513,072 on Google Patents ↗ Look up on USPTO ↗