Live analysis

13,400

13,400 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.).

13,400 (thirteen thousand four hundred) is an even 5-digit number. It is a composite number with 24 divisors, and factors as 2³ × 5² × 67. Its proper divisors sum to 18,220, more than the number itself, making it an abundant number. Written other ways, in hexadecimal, 0x3458.

Abundant Number Evil Number Gapful Number Harshad / Niven Practical Number Recamán's Sequence Semiperfect Number

Interestingness

★ ★ ★ ☆ ☆

5 notable facts · grade C

13,388 13,389 13,390 13,391 13,392 13,393 13,394 13,395 13,396 13,397 13,398 13,399 13,400 13,401 13,402 13,403 13,404 13,405 13,406 13,407 13,408 13,409 13,410 13,411 13,412

less more

Properties

Parity: Even
Digit count: 5
Digit sum: 8
Digit product: 0
Digital root: 8
Palindrome: No
Bit width: 14 bits
Reversed: 431
Recamán's sequence: a(47,475) = 13,400
Square (n²): 179,560,000
Cube (n³): 2,406,104,000,000
Divisor count: 24
σ(n) — sum of divisors: 31,620
φ(n) — Euler's totient: 5,280
Sum of prime factors: 83

Primality

Prime factorization: 2 ³ × 5 ² × 67

Nearest primes: 13,399 (−1) · 13,411 (+11)

Divisors & multiples

All divisors (24)

1 · 2 · 4 · 5 · 8 · 10 · 20 · 25 · 40 · 50 · 67 · 100 · 134 · 200 · 268 · 335 · 536 · 670 · 1340 · 1675 · 2680 · 3350 · 6700 (half) · 13400

Aliquot sum (sum of proper divisors): 18,220

Factor pairs (a × b = 13,400)

1 × 13400

2 × 6700

4 × 3350

5 × 2680

8 × 1675

10 × 1340

20 × 670

25 × 536

40 × 335

50 × 268

67 × 200

100 × 134

First multiples

13,400 · 26,800 (double) · 40,200 · 53,600 · 67,000 · 80,400 · 93,800 · 107,200 · 120,600 · 134,000

Sums & aliquot sequence

As consecutive integers: 2,678 + 2,679 + 2,680 + 2,681 + 2,682 830 + 831 + … + 845 524 + 525 + … + 548 167 + 168 + … + 233

Aliquot sequence: 13,400 → 18,220 → 20,084 → 15,070 → 14,738 → 7,372 → 6,348 → 9,136 → 8,596 → 8,652 → 14,644 → 14,700 → 34,776 → 80,424 → 137,586 → 149,838 → 194,898 — unresolved within range

Continued fraction of √n

√13,400 = [115; (1, 3, 7, 4, 1, 1, 2, 2, 1, 1, 1, 8, 1, 1, 1, 2, 2, 1, 1, 4, 7, 3, 1, 230)]

Period length 24 — the block in parentheses repeats forever.

Representations

In words: thirteen thousand four hundred
Ordinal: 13400th
Binary: 11010001011000
Octal: 32130
Hexadecimal: 0x3458
Base64: NFg=
One's complement: 52,135 (16-bit)
Scientific notation: 1.34 × 10⁴
As a duration: 13,400 s = 3 hours, 43 minutes, 20 seconds

In other bases

ternary (3) 200101022

quaternary (4) 3101120

quinary (5) 412100

senary (6) 142012

septenary (7) 54032

nonary (9) 20338

undecimal (11) a082

duodecimal (12) 7908

tridecimal (13) 613a

tetradecimal (14) 4c52

pentadecimal (15) 3e85

As an angle

13,400° = 37 × 360° + 80°

80° ≈ 1.396 rad

Compass bearing: E (east)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹𒁹 𒌋𒌋𒌋𒌋𒁹𒁹𒁹 𒌋𒌋
Egyptian hieroglyphic: 𓂍𓆼𓆼𓆼𓍢𓍢𓍢𓍢
Greek (Milesian): ͵ιγυʹ
Mayan (base 20): 𝋡·𝋭·𝋪·𝋠
Chinese: 一萬三千四百
Chinese (financial): 壹萬參仟肆佰

In other modern scripts

Eastern Arabic ١٣٤٠٠ Devanagari १३४०० Bengali ১৩৪০০ Tamil ௧௩௪௦௦ Thai ๑๓๔๐๐ Tibetan ༡༣༤༠༠ Khmer ១៣៤០០ Lao ໑໓໔໐໐ Burmese ၁၃၄၀၀

Digit at this position in famous constants

π — Pi (π): Digit 13,400 = 1
e — Euler's number (e): Digit 13,400 = 2
φ — Golden ratio (φ): Digit 13,400 = 8
√2 — Pythagoras's (√2): Digit 13,400 = 7
ln 2 — Natural log of 2: Digit 13,400 = 3
γ — Euler-Mascheroni (γ): Digit 13,400 = 0

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 13400, here are decompositions:

3 + 13397 = 13400
19 + 13381 = 13400
61 + 13339 = 13400
73 + 13327 = 13400
103 + 13297 = 13400
109 + 13291 = 13400
151 + 13249 = 13400
181 + 13219 = 13400

Showing the first eight; more decompositions exist.

Unicode codepoint

㑘

CJK Unified Ideograph-3458

U+3458

Other letter (Lo)

UTF-8 encoding: E3 91 98 (3 bytes).

Lookup U+3458 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#003458

RGB(0, 52, 88)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.52.88.

Address: 0.0.52.88
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.52.88

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

Musical pitch

Heard as a frequency, 13,400 Hz is closest to:

Concert pitch (A4 = 440 Hz): G♯9 (13289.8 Hz, +14¢)
Scientific pitch (C4 = 256 Hz): A9 (13777.2 Hz, -48¢ — about midway to G♯9)
Baroque pitch (A4 = 415 Hz): A9 (13280 Hz, +16¢)

Position in π

The digit sequence 13400 first appears in π at position 44,939 of the decimal expansion (the 44,939ordinal-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 13400 on Pi Search ↗