text: # 81 (number)
  
  81 is an odd two-digits composite number following 80 and preceding 82. In scientific notation, it is written as 8.1 × 101. The sum of its digits is 9. It has a total of 4 prime factors and 5 positive divisors. There are 54 positive integers (up to 81) that are relatively prime to 81.
  
  ## Basic properties
  
  • Is Prime? no
  • Number parity odd
  • Number length 2
  • Sum of Digits 9
  • Digital Root 9
  
  ## Name
  
  Name eighty-one
  
  ## Notation
  
  Scientific notation 8.1 × 101 81 × 100
  
  ## Prime Factorization of 81
  
  Prime Factorization 34
  
  Composite number
  Distinct Factors Total Factors Radical ω 1 Total number of distinct prime factors Ω 4 Total number of prime factors rad 3 Product of the distinct prime numbers λ 1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ 0 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ 1.09861 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0
  
  The prime factorization of 81 is 34. Since it has a total of 4 prime factors, 81 is a composite number.
  
  ## Divisors of 81
  
  1, 3, 9, 27, 81
  
  5 divisors
  
   Even divisors 0 5 3 2
  Total Divisors Sum of Divisors Aliquot Sum τ 5 Total number of the positive divisors of n σ 121 Sum of all the positive divisors of n s 40 Sum of the proper positive divisors of n A 24.2 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G 9 Returns the nth root of the product of n divisors H 3.34711 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors
  
  The number 81 can be divided by 5 positive divisors (out of which none is even, and 5 are odd). The sum of these divisors (counting 81) is 121, the average is 24.2.
  
  ## Other Arithmetic Functions (n = 81)
  
  1 φ(n) n
  Euler Totient Carmichael Lambda Prime Pi φ 54 Total number of positive integers not greater than n that are coprime to n λ 54 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π ≈ 22 Total number of primes less than or equal to n r2 4 The number of ways n can be represented as the sum of 2 squares
  
  There are 54 positive integers (less than 81) that are coprime with 81. And there are approximately 22 prime numbers less than or equal to 81.
  
  ## Divisibility of 81
  
  m n mod m
  2 1
  3 0
  4 1
  5 1
  6 3
  7 4
  8 1
  9 0
  
  The number 81 is divisible by 3 and 9.
  
  ## Classification of 81
  
  • Deficient
  
  ### Expressible via specific sums
  
  • Polite
  • Non hypotenuse
  
  • Square
  • Heptagonal
  
  ### By Shape (2D, centered)
  
  • Centered Octagonal
  
  ### By Powers
  
  • Powerful
  • Prime Power
  • Perfect Power
  • Perfect Square
  
  • Frugal
  • Regular
  
  ## Base conversion 81
  
  Base System Value
  2 Binary 1010001
  3 Ternary 10000
  4 Quaternary 1101
  5 Quinary 311
  6 Senary 213
  8 Octal 121
  10 Decimal 81
  12 Duodecimal 69
  20 Vigesimal 41
  36 Base36 29
  
  ## Basic calculations (n = 81)
  
  ### Multiplication
  
  n×y
   n×2 162 243 324 405
  
  ### Division
  
  n÷y
   n÷2 40.5 27 20.25 16.2
  
  ### Exponentiation
  
  ny
   n2 6561 531441 43046721 3486784401
  
  ### Nth Root
  
  y√n
   2√n 9 4.32675 3 2.40822
  
  ## 81 as geometric shapes
  
  ### Circle
  
   Diameter 162 508.938 20612
  
  ### Sphere
  
   Volume 2.22609e+06 82448 508.938
  
  ### Square
  
  Length = n
   Perimeter 324 6561 114.551
  
  ### Cube
  
  Length = n
   Surface area 39366 531441 140.296
  
  ### Equilateral Triangle
  
  Length = n
   Perimeter 243 2841 70.1481
  
  ### Triangular Pyramid
  
  Length = n
   Surface area 11364 62630.9 66.1362
  
  ## Cryptographic Hash Functions
  
  md5 43ec517d68b6edd3015b3edc9a11367b 1d513c0bcbe33b2e7440e5e14d0b22ef95c9d673 5316ca1c5ddca8e6ceccfce58f3b8540e540ee22f6180fb89492904051b3d531 a4a3cd6ad27b0a593f5c188086978992fef71b22aa5e4211646c62c9c031dc32e301c56a3513ca811b2725eca01e09f7eefafaa65af129050beea4938ffa18ca 72ac3367c48e0516e8f40a414454a9442b5730c9