13,824
13,824 is a composite number, even.
13,824 (thirteen thousand eight hundred twenty-four) is an even 5-digit number. It is a composite number with 40 divisors, and factors as 2⁹ × 3³. Its proper divisors sum to 27,096, more than the number itself, making it an abundant number. It is a perfect cube (24³). Written other ways, in hexadecimal, 0x3600.
Interestingness
Properties
- Parity
- Even
- Digit count
- 5
- Digit sum
- 18
- Digit product
- 192
- Digital root
- 9
- Palindrome
- No
- Bit width
- 14 bits
- Reversed
- 42,831
- Recamán's sequence
- a(21,068) = 13,824
- Square (n²)
- 191,102,976
- Cube (n³)
- 2,641,807,540,224
- Cube root (∛n)
- 24
- Divisor count
- 40
- σ(n) — sum of divisors
- 40,920
- φ(n) — Euler's totient
- 4,608
- Sum of prime factors
- 27
Primality
Prime factorization: 2 9 × 3 3
Divisors & multiples
Sums & aliquot sequence
Continued fraction of √n
√13,824 = [117; (1, 1, 2, 1, 4, 3, 2, 6, 10, 14, 1, 1, 2, 25, 1, 2, 1, 2, 2, 8, 1, 57, 1, 8, …)]
Period length 44 — the block in parentheses repeats forever.
Representations
- In words
- thirteen thousand eight hundred twenty-four
- Ordinal
- 13824th
- Binary
- 11011000000000
- Octal
- 33000
- Hexadecimal
- 0x3600
- Base64
- NgA=
- One's complement
- 51,711 (16-bit)
- Scientific notation
- 1.3824 × 10⁴
- As a duration
- 13,824 s = 3 hours, 50 minutes, 24 seconds
As an angle
Historical numeral systems
- Babylonian (base 60)
- 𒁹𒁹𒁹 𒌋𒌋𒌋𒌋𒌋 𒌋𒌋𒁹𒁹𒁹𒁹
- Egyptian hieroglyphic
- 𓂍𓆼𓆼𓆼𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓎆𓎆𓏺𓏺𓏺𓏺
- Greek (Milesian)
- ͵ιγωκδʹ
- Mayan (base 20)
- 𝋡·𝋮·𝋫·𝋤
- Chinese
- 一萬三千八百二十四
- Chinese (financial)
- 壹萬參仟捌佰貳拾肆
Digit at this position in famous constants
- π — Pi (π)
- Digit 13,824 = 7
- e — Euler's number (e)
- Digit 13,824 = 4
- φ — Golden ratio (φ)
- Digit 13,824 = 7
- √2 — Pythagoras's (√2)
- Digit 13,824 = 4
- ln 2 — Natural log of 2
- Digit 13,824 = 2
- γ — Euler-Mascheroni (γ)
- Digit 13,824 = 2
Also seen as
Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 13824, here are decompositions:
- 17 + 13807 = 13824
- 43 + 13781 = 13824
- 61 + 13763 = 13824
- 67 + 13757 = 13824
- 73 + 13751 = 13824
- 101 + 13723 = 13824
- 103 + 13721 = 13824
- 113 + 13711 = 13824
Showing the first eight; more decompositions exist.
UTF-8 encoding: E3 98 80 (3 bytes).
As an unsigned 32-bit integer, this is the IPv4 address 0.0.54.0.
- Address
- 0.0.54.0
- Class
- reserved
- IPv4-mapped IPv6
- ::ffff:0.0.54.0
Unspecified address (0.0.0.0/8) — "this network" placeholder.
Heard as a frequency, 13,824 Hz is closest to:
- Concert pitch (A4 = 440 Hz): A9 (14080 Hz, -32¢)
- Scientific pitch (C4 = 256 Hz): A9 (13777.2 Hz, +6¢)
- Baroque pitch (A4 = 415 Hz): A♯9 (14069.7 Hz, -30¢)
The digit sequence 13824 first appears in π at position 186,286 of the decimal expansion (the 186,286ordinal-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.
Related reading
- Babylonian numerals — The base-60 cuneiform system that gave us 60 minutes, 60 seconds, and 360°.