Live analysis

5,040

5,040 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.).

5,040 (five thousand forty) is an even 4-digit number. It is a composite number with 60 divisors, and factors as 2⁴ × 3² × 5 × 7. Its proper divisors sum to 14,304, more than the number itself, making it an abundant number. It is a factorial (7! = 5,040). Written other ways, in hexadecimal, 0x13B0.

Abundant Number Evil Number Factorial Harshad / Niven Highly Abundant Highly Composite Number Practical Number Recamán's Sequence Refactorable Number Semiperfect Number

Interestingness

★ ★ ★ ★ ★

8 notable facts · grade A

5,028 5,029 5,030 5,031 5,032 5,033 5,034 5,035 5,036 5,037 5,038 5,039 5,040 5,041 5,042 5,043 5,044 5,045 5,046 5,047 5,048 5,049 5,050 5,051 5,052

less more

Properties

Parity: Even
Digit count: 4
Digit sum: 9
Digit product: 0
Digital root: 9
Palindrome: No
Bit width: 13 bits
Reversed: 405
Recamán's sequence: a(1,996) = 5,040
Square (n²): 25,401,600
Cube (n³): 128,024,064,000
Divisor count: 60
σ(n) — sum of divisors: 19,344
φ(n) — Euler's totient: 1,152
Sum of prime factors: 26

Primality

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

Nearest primes: 5,039 (−1) · 5,051 (+11)

Divisors & multiples

All divisors (60)

1 · 2 · 3 · 4 · 5 · 6 · 7 · 8 · 9 · 10 · 12 · 14 · 15 · 16 · 18 · 20 · 21 · 24 · 28 · 30 · 35 · 36 · 40 · 42 · 45 · 48 · 56 · 60 · 63 · 70 · 72 · 80 · 84 · 90 · 105 · 112 · 120 · 126 · 140 · 144 · 168 · 180 · 210 · 240 · 252 · 280 · 315 · 336 · 360 · 420 · 504 · 560 · 630 · 720 · 840 · 1008 · 1260 · 1680 · 2520 (half) · 5040

Aliquot sum (sum of proper divisors): 14,304

Factor pairs (a × b = 5,040)

1 × 5040

2 × 2520

3 × 1680

4 × 1260

5 × 1008

6 × 840

7 × 720

8 × 630

9 × 560

10 × 504

12 × 420

14 × 360

15 × 336

16 × 315

18 × 280

20 × 252

21 × 240

24 × 210

28 × 180

30 × 168

35 × 144

36 × 140

40 × 126

42 × 120

45 × 112

48 × 105

56 × 90

60 × 84

63 × 80

70 × 72

First multiples

5,040 · 10,080 (double) · 15,120 · 20,160 · 25,200 · 30,240 · 35,280 · 40,320 · 45,360 · 50,400

Sums & aliquot sequence

As consecutive integers: 1,679 + 1,680 + 1,681 1,006 + 1,007 + 1,008 + 1,009 + 1,010 717 + 718 + … + 723 556 + 557 + … + 564

Aliquot sequence: 5,040 → 14,304 → 23,496 → 41,304 → 62,016 → 120,864 → 196,656 → 343,488 → 565,832 → 495,118 → 316,322 → 158,164 → 118,630 → 94,922 → 52,150 → 59,450 → 57,730 — unresolved within range

Continued fraction of √n

√5,040 = [70; (1, 140)]

Period length 2 — the block in parentheses repeats forever.

Representations

In words: five thousand forty
Ordinal: 5040th
Binary: 1001110110000
Octal: 11660
Hexadecimal: 0x13B0
Base64: E7A=
One's complement: 60,495 (16-bit)
Scientific notation: 5.04 × 10³
As a duration: 5,040 s = 1 hour, 24 minutes

In other bases

ternary (3) 20220200

quaternary (4) 1032300

quinary (5) 130130

senary (6) 35200

septenary (7) 20460

nonary (9) 6820

undecimal (11) 3872

duodecimal (12) 2b00

tridecimal (13) 23a9

tetradecimal (14) 1ba0

pentadecimal (15) 1760

As an angle

5,040° = 14 × 360°

0° ≈ 0 rad

Compass bearing: N (north)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹 𒌋𒌋𒁹𒁹𒁹𒁹 ·
Egyptian hieroglyphic: 𓆼𓆼𓆼𓆼𓆼𓎆𓎆𓎆𓎆
Greek (Milesian): ͵εμʹ
Mayan (base 20): 𝋬·𝋬·𝋠
Chinese: 五千零四十
Chinese (financial): 伍仟零肆拾

In other modern scripts

Eastern Arabic ٥٠٤٠ Devanagari ५०४० Bengali ৫০৪০ Tamil ௫௦௪௦ Thai ๕๐๔๐ Tibetan ༥༠༤༠ Khmer ៥០៤០ Lao ໕໐໔໐ Burmese ၅၀၄၀

Digit at this position in famous constants

π — Pi (π): Digit 5,040 = 8
e — Euler's number (e): Digit 5,040 = 0
φ — Golden ratio (φ): Digit 5,040 = 8
√2 — Pythagoras's (√2): Digit 5,040 = 8
ln 2 — Natural log of 2: Digit 5,040 = 4
γ — Euler-Mascheroni (γ): Digit 5,040 = 6

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 5040, here are decompositions:

17 + 5023 = 5040
19 + 5021 = 5040
29 + 5011 = 5040
31 + 5009 = 5040
37 + 5003 = 5040
41 + 4999 = 5040
47 + 4993 = 5040
53 + 4987 = 5040

Showing the first eight; more decompositions exist.

Unicode codepoint

Ꮀ

Cherokee Letter Ho

U+13B0

Uppercase letter (Lu)

UTF-8 encoding: E1 8E B0 (3 bytes).

Lookup U+13B0 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#0013B0

RGB(0, 19, 176)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.19.176.

Address: 0.0.19.176
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.19.176

Unspecified address (0.0.0.0/8) — "this network" placeholder.

Musical pitch

Heard as a frequency, 5,040 Hz is closest to:

Concert pitch (A4 = 440 Hz): D♯8 (4978 Hz, +21¢)
Scientific pitch (C4 = 256 Hz): E8 (5160.6 Hz, -41¢)
Baroque pitch (A4 = 415 Hz): E8 (4974.4 Hz, +23¢)

Position in π

The digit sequence 5040 first appears in π at position 14,369 of the decimal expansion (the 14,369ordinal-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 5040 on Pi Search ↗