Live analysis

488,448

488,448 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.).

488,448 (four hundred eighty-eight thousand four hundred forty-eight) is an even 6-digit number. It is a composite number with 66 divisors, and factors as 2¹⁰ × 3² × 53. Its proper divisors sum to 948,546, more than the number itself, making it an abundant number. Written other ways, in hexadecimal, 0x77400.

Abundant Number Gapful Number Harshad / Niven Odious Number Pernicious Number Practical Number Weird Number

Interestingness

★ ★ ☆ ☆ ☆

4 notable facts · grade D

488,436 488,437 488,438 488,439 488,440 488,441 488,442 488,443 488,444 488,445 488,446 488,447 488,448 488,449 488,450 488,451 488,452 488,453 488,454 488,455 488,456 488,457 488,458 488,459 488,460

less more

Properties

Parity: Even
Digit count: 6
Digit sum: 36
Digit product: 32,768
Digital root: 9
Palindrome: No
Bit width: 19 bits
Reversed: 844,884
Square (n²): 238,581,448,704
Cube (n³): 116,534,631,456,571,392
Divisor count: 66
σ(n) — sum of divisors: 1,436,994
φ(n) — Euler's totient: 159,744
Sum of prime factors: 79

Primality

Prime factorization: 2 ¹⁰ × 3 ² × 53

Nearest primes: 488,441 (−7) · 488,459 (+11)

Divisors & multiples

All divisors (66)

1 · 2 · 3 · 4 · 6 · 8 · 9 · 12 · 16 · 18 · 24 · 32 · 36 · 48 · 53 · 64 · 72 · 96 · 106 · 128 · 144 · 159 · 192 · 212 · 256 · 288 · 318 · 384 · 424 · 477 · 512 · 576 · 636 · 768 · 848 · 954 · 1024 · 1152 · 1272 · 1536 · 1696 · 1908 · 2304 · 2544 · 3072 · 3392 · 3816 · 4608 · 5088 · 6784 · 7632 · 9216 · 10176 · 13568 · 15264 · 20352 · 27136 · 30528 · 40704 · 54272 · 61056 · 81408 · 122112 · 162816 · 244224 (half) · 488448

Aliquot sum (sum of proper divisors): 948,546

Factor pairs (a × b = 488,448)

1 × 488448

2 × 244224

3 × 162816

4 × 122112

6 × 81408

8 × 61056

9 × 54272

12 × 40704

16 × 30528

18 × 27136

24 × 20352

32 × 15264

36 × 13568

48 × 10176

53 × 9216

64 × 7632

72 × 6784

96 × 5088

106 × 4608

128 × 3816

144 × 3392

159 × 3072

192 × 2544

212 × 2304

256 × 1908

288 × 1696

318 × 1536

384 × 1272

424 × 1152

477 × 1024

512 × 954

576 × 848

636 × 768

First multiples

488,448 · 976,896 (double) · 1,465,344 · 1,953,792 · 2,442,240 · 2,930,688 · 3,419,136 · 3,907,584 · 4,396,032 · 4,884,480

Sums & aliquot sequence

As a sum of two squares: 192² + 672²

As consecutive integers: 162,815 + 162,816 + 162,817 54,268 + 54,269 + … + 54,276 9,190 + 9,191 + … + 9,242 2,993 + 2,994 + … + 3,151

Aliquot sequence: 488,448 → 948,546 → 1,106,676 → 1,762,764 → 2,592,804 → 3,483,196 → 2,874,260 → 3,211,540 → 3,602,540 → 4,380,820 → 4,818,944 → 5,615,116 → 5,102,948 → 3,827,218 → 1,913,612 → 1,435,216 → 1,364,208 — unresolved within range

Continued fraction of √n

√488,448 = [698; (1, 8, 7, 3, 11, 2, 2, 1, 21, 2, 9, 3, 2, 86, 1, 13, 2, 2, 1, 2, 5, 5, 1, 1, …)]

Representations

In words: four hundred eighty-eight thousand four hundred forty-eight
Ordinal: 488448th
Binary: 1110111010000000000
Octal: 1672000
Hexadecimal: 0x77400
Base64: B3QA
One's complement: 4,294,478,847 (32-bit)
Scientific notation: 4.88448 × 10⁵
As a duration: 488,448 s = 5 days, 15 hours, 40 minutes, 48 seconds

In other bases

ternary (3) 220211000200

quaternary (4) 1313100000

quinary (5) 111112243

senary (6) 14245200

septenary (7) 4103022

nonary (9) 824020

undecimal (11) 303a84

duodecimal (12) 1b6800

tridecimal (13) 14142c

tetradecimal (14) ca012

pentadecimal (15) 99ad3

As an angle

488,448° = 1,356 × 360° + 288°

288° ≈ 5.027 rad

Compass bearing: WNW (west-northwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹 𒌋𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒌋𒌋 𒌋𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓆐𓆐𓆐𓆐𓂍𓂍𓂍𓂍𓂍𓂍𓂍𓂍𓆼𓆼𓆼𓆼𓆼𓆼𓆼𓆼𓍢𓍢𓍢𓍢𓎆𓎆𓎆𓎆𓏺𓏺𓏺𓏺𓏺𓏺𓏺𓏺
Greek (Milesian): ͵υπηυμηʹ
Chinese: 四十八萬八千四百四十八
Chinese (financial): 肆拾捌萬捌仟肆佰肆拾捌

In other modern scripts

Eastern Arabic ٤٨٨٤٤٨ Devanagari ४८८४४८ Bengali ৪৮৮৪৪৮ Tamil ௪௮௮௪௪௮ Thai ๔๘๘๔๔๘ Tibetan ༤༨༨༤༤༨ Khmer ៤៨៨៤៤៨ Lao ໔໘໘໔໔໘ Burmese ၄၈၈၄၄၈

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 488448, here are decompositions:

7 + 488441 = 488448
29 + 488419 = 488448
31 + 488417 = 488448
41 + 488407 = 488448
47 + 488401 = 488448
67 + 488381 = 488448
101 + 488347 = 488448
109 + 488339 = 488448

Showing the first eight; more decompositions exist.

Hex color

#077400

RGB(7, 116, 0)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.7.116.0.

Address: 0.7.116.0
Class: reserved
IPv4-mapped IPv6: ::ffff:0.7.116.0

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 488,448 and was likely granted around 1892.

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

Look up US488,448 on Google Patents ↗ Look up on USPTO ↗

Position in π

The digit sequence 488448 first appears in π at position 800,694 of the decimal expansion (the 800,694ordinal-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.

Look up 488448 on Pi Search ↗