# 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
The provided text passage is a detailed mathematical description of the number 81, including its properties, factorization, divisors, and various representations. It does not contain any specific mathematical questions or answers to such questions.
no_question
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
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- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# 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
user
The provided text passage is a detailed mathematical description of the number 81, including its properties, factorization, divisors, and various representations. It does not contain any specific mathematical questions or answers to such questions.

TYPE: NO_QUESTION