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40,320

40,320 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.).
Abundant Number Evil Number Factorial Gapful Number Harshad / Niven Practical Number Weird Number

Properties

Parity
Even
Digit count
5
Digit sum
9
Digit product
0
Digital root
9
Palindrome
No
Bit width
16 bits
Reversed
2,304
Square (n²)
1,625,702,400
Cube (n³)
65,548,320,768,000
Divisor count
96
σ(n) — sum of divisors
159,120
φ(n) — Euler's totient
9,216
Sum of prime factors
32

Primality

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

Nearest primes: 40,289 (−31) · 40,343 (+23)

Divisors & multiples

All divisors (96)
1 · 2 · 3 · 4 · 5 · 6 · 7 · 8 · 9 · 10 · 12 · 14 · 15 · 16 · 18 · 20 · 21 · 24 · 28 · 30 · 32 · 35 · 36 · 40 · 42 · 45 · 48 · 56 · 60 · 63 · 64 · 70 · 72 · 80 · 84 · 90 · 96 · 105 · 112 · 120 · 126 · 128 · 140 · 144 · 160 · 168 · 180 · 192 · 210 · 224 · 240 · 252 · 280 · 288 · 315 · 320 · 336 · 360 · 384 · 420 · 448 · 480 · 504 · 560 · 576 · 630 · 640 · 672 · 720 · 840 · 896 · 960 · 1008 · 1120 · 1152 · 1260 · 1344 · 1440 · 1680 · 1920 · 2016 · 2240 · 2520 · 2688 · 2880 · 3360 · 4032 · 4480 · 5040 · 5760 · 6720 · 8064 · 10080 · 13440 · 20160 (half) · 40320
Aliquot sum (sum of proper divisors): 118,800
Factor pairs (a × b = 40,320)
1 × 40320
2 × 20160
3 × 13440
4 × 10080
5 × 8064
6 × 6720
7 × 5760
8 × 5040
9 × 4480
10 × 4032
12 × 3360
14 × 2880
15 × 2688
16 × 2520
18 × 2240
20 × 2016
21 × 1920
24 × 1680
28 × 1440
30 × 1344
32 × 1260
35 × 1152
36 × 1120
40 × 1008
42 × 960
45 × 896
48 × 840
56 × 720
60 × 672
63 × 640
64 × 630
70 × 576
72 × 560
80 × 504
84 × 480
90 × 448
96 × 420
105 × 384
112 × 360
120 × 336
126 × 320
128 × 315
140 × 288
144 × 280
160 × 252
168 × 240
180 × 224
192 × 210
First multiples
40,320 · 80,640 (double) · 120,960 · 161,280 · 201,600 · 241,920 · 282,240 · 322,560 · 362,880 · 403,200

Sums & aliquot sequence

As consecutive integers: 13,439 + 13,440 + 13,441 8,062 + 8,063 + 8,064 + 8,065 + 8,066 5,757 + 5,758 + … + 5,763 4,476 + 4,477 + … + 4,484
Aliquot sequence: 40,320 118,800 342,480 719,952 1,181,712 2,308,144 2,163,916 1,643,916 2,191,916 1,893,844 1,594,956 2,574,132 3,978,540 9,033,732 16,027,668 26,871,552 52,047,288 — unresolved within range

Representations

In words
forty thousand three hundred twenty
Ordinal
40320th
Binary
1001110110000000
Octal
116600
Hexadecimal
0x9D80
Base64
nYA=
One's complement
25,215 (16-bit)
In other bases
ternary (3) 2001022100
quaternary (4) 21312000
quinary (5) 2242240
senary (6) 510400
septenary (7) 225360
nonary (9) 61270
undecimal (11) 28325
duodecimal (12) 1b400
tridecimal (13) 15477
tetradecimal (14) 109a0
pentadecimal (15) be30

Historical numeral systems

Babylonian (base 60)
𒌋𒁹 𒌋𒁹𒁹 ·
Egyptian hieroglyphic
𓂍𓂍𓂍𓂍𓍢𓍢𓍢𓎆𓎆
Greek (Milesian)
͵μτκʹ
Mayan (base 20)
𝋥·𝋠·𝋰·𝋠
Chinese
四萬零三百二十
Chinese (financial)
肆萬零參佰貳拾
In other modern scripts
Eastern Arabic ٤٠٣٢٠ Devanagari ४०३२० Bengali ৪০৩২০ Tamil ௪௦௩௨௦ Thai ๔๐๓๒๐ Tibetan ༤༠༣༢༠ Khmer ៤០៣២០ Lao ໔໐໓໒໐ Burmese ၄၀၃၂၀

Digit at this position in famous constants

π — Pi (π)
Digit 40,320 = 7
e — Euler's number (e)
Digit 40,320 = 4
φ — Golden ratio (φ)
Digit 40,320 = 1
√2 — Pythagoras's (√2)
Digit 40,320 = 5
ln 2 — Natural log of 2
Digit 40,320 = 8
γ — Euler-Mascheroni (γ)
Digit 40,320 = 3

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 40320, here are decompositions:

  • 31 + 40289 = 40320
  • 37 + 40283 = 40320
  • 43 + 40277 = 40320
  • 67 + 40253 = 40320
  • 79 + 40241 = 40320
  • 83 + 40237 = 40320
  • 89 + 40231 = 40320
  • 107 + 40213 = 40320

Showing the first eight; more decompositions exist.

Unicode codepoint
CJK Unified Ideograph-9D80
U+9D80
Other letter (Lo)

UTF-8 encoding: E9 B6 80 (3 bytes).

Hex color
#009D80
RGB(0, 157, 128)
IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.157.128.

Address
0.0.157.128
Class
reserved
IPv4-mapped IPv6
::ffff:0.0.157.128

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

Position in π

The digit sequence 40320 first appears in π at position 168,257 of the decimal expansion (the 168,257ordinal-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.