Numerical properties of 8
Show numerical properties of 8
We start by listing out divisors for 8
| Divisor | Divisor Math |
|---|---|
| 1 | 8 ÷ 1 = 8 |
| 2 | 8 ÷ 2 = 4 |
| 4 | 8 ÷ 4 = 2 |
Positive or Negative Number Test:
Positive Numbers > 0Since 8 ≥ 0 and it is an integer
8 is a positive number
Whole Number Test:
Positive numbers including 0with no decimal or fractions
Since 8 ≥ 0 and it is an integer
8 is a whole number
Prime or Composite Test:
Since 8 has divisors other than 1 and itself
it is a composite number
Perfect/Deficient/Abundant Test:
Calculate divisor sum D
If D = N, then it's perfect
If D > N, then it's abundant
If D < N, then it's deficient
Divisor Sum = 1 + 2 + 4
Divisor Sum = 7
Since our divisor sum of 7 < 8
8 is a deficient number!
Odd or Even Test (Parity Function):
A number is even if it is divisible by 2
If not divisible by 2, it is odd
| 4 = | 8 |
| 2 |
Since 4 is an integer, 8 is divisible by 2
it is an even number
This can be written as A(8) = Even
Evil or Odious Test:
Get binary expansion
If binary has even amount 1's, then it's evil
If binary has odd amount 1's, then it's odious
8 to binary = 1000
There are 1 1's, 8 is an odious number
Triangular Test:
Can you stack numbers in a pyramid?
Each row above has one item less than the row before it
Using a bottom row of 4 items, we cannot form a pyramid
8 is not triangular
Triangular number:
Rectangular Test:
Is there an integer m such that n = m(m + 1)
No integer m exists such that m(m + 1) = 8
8 is not rectangular
Rectangular number:
Automorphic (Curious) Test:
Does n2 ends with n
82 = 8 x 8 = 64
Since 64 does not end with 8
it is not automorphic (curious)
Automorphic number:
Undulating Test:
Do the digits of n alternate in the form abab
Since 8 < 100
We only perform the test on numbers > 99
Square Test:
Is there a number m such that m2 = n?
22 = 4 and 32 = 9 which do not equal 8
Therefore, 8 is not a square
Cube Test:
Is there a number m such that m3 = n
23 = 8
Since 8 is the cube of 2
8 is a cube
Palindrome Test:
Is the number read backwards equal to the number?
The number read backwards is 8
Since 8 is the same backwards and forwards
it is a palindrome
Palindromic Prime Test:
Is it both prime and a palindrome
From above, since 8 is not both prime and a palindrome
it is NOT a palindromic prime
Repunit Test:
A number is repunit if every digit is equal to 1
Since there is at least one digit in 8 ≠ 1
then it is NOT repunit
Apocalyptic Power Test:
Does 2n contain the consecutive digits 666?
28 = 256
Since 28 does not have 666
8 is NOT an apocalyptic power
Pentagonal Test:
It satisfies the form:
| n(3n - 1) | |
| 2 |
Check values of 2 and 3
Using n = 3, we have:
| 3(3(3 - 1) | |
| 2 |
12 ← Since this does not equal 8
this is NOT a pentagonal number
Using n = 2, we have:
| 2(3(2 - 1) | |
| 2 |
5 ← Since this does not equal 8
this is NOT a pentagonal number
Pentagonal number:
Hexagonal Test:
Is there an integer m such that n = m(2m - 1)
No integer m exists such that m(2m - 1) = 8
Therefore 8 is not hexagonal
Hexagonal number:
Heptagonal Test:
Is there an integer m such that:
| m = | n(5n - 3) |
| 2 |
No integer m exists such that m(5m - 3)/2 = 8
Therefore 8 is not heptagonal
Heptagonal number:
Octagonal Test:
Is there an integer m such that n = m(3m - 3)
The integer m = 2 is octagonal
Since 2(3(2) - 2) = 8
Octagonal number:
Nonagonal Test:
Is there an integer m such that:
| m = | n(7n - 5) |
| 2 |
No integer m exists such that m(7m - 5)/2 = 8
Therefore 8 is not nonagonal
Nonagonal number:
Tetrahedral (Pyramidal) Test:
Tetrahederal numbers satisfy the form:
| n(n + 1)(n + 2) | |
| 6 |
Check values of 2 and 3
Using n = 3, we have:
| 3(3 + 1)(3 + 2) | |
| 6 |
10 ← Since this does not equal 8
This is NOT a tetrahedral (Pyramidal) number
Using n = 2, we have:
| 2(2 + 1)(2 + 2) | |
| 6 |
4 ← Since this does not equal 8
This is NOT a tetrahedral (Pyramidal) number
Narcissistic (Plus Perfect) Test:
Is equal to the square sum of it's m-th powers of its digits
8 is a 1 digit number, so m = 1
Square sum of digitsm = 81
Square sum of digitsm = 8
Square sum of digitsm = 8
Since 8 = 8
8 is narcissistic (plus perfect)
Catalan Test:
| Cn = | 2n! |
| (n + 1)!n! |
Check values of 3 and 4
Using n = 4, we have:
| C4 = | (2 x 4)! |
| 4!(4 + 1)! |
Using our factorial lesson
| C4 = | 8! |
| 4!5! |
| C4 = | 40320 |
| (24)(120) |
| C4 = | 40320 |
| 2880 |
C4 = 14
Since this does not equal 8
This is NOT a Catalan number
Using n = 3, we have:
| C3 = | (2 x 3)! |
| 3!(3 + 1)! |
Using our factorial lesson
| C3 = | 6! |
| 3!4! |
| C3 = | 720 |
| (6)(24) |
| C3 = | 720 |
| 144 |
C3 = 5
Since this does not equal 8
This is NOT a Catalan number
Number Properties for 8
Final Answer
Positive
Whole
Composite
Deficient
Even
Odious
Cube
Palindrome
Octagonal
Narcissistic (Plus Perfect)
You have 1 free calculations remaining
What is the Answer?
Positive
Whole
Composite
Deficient
Even
Odious
Cube
Palindrome
Octagonal
Narcissistic (Plus Perfect)
How does the Number Property Calculator work?
Free Number Property Calculator - This calculator determines if an integer you entered has any of the following properties:
* Even Numbers or Odd Numbers (Parity Function or even-odd numbers)
* Evil Numbers or Odious Numbers
* Perfect Numbers, Abundant Numbers, or Deficient Numbers
* Triangular Numbers
* Prime Numbers or Composite Numbers
* Automorphic (Curious)
* Undulating Numbers
* Square Numbers
* Cube Numbers
* Palindrome Numbers
* Repunit Numbers
* Apocalyptic Power
* Pentagonal
* Tetrahedral (Pyramidal)
* Narcissistic (Plus Perfect)
* Catalan
* Repunit
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What 5 formulas are used for the Number Property Calculator?
Positive Numbers are greater than 0Whole Numbers are positive numbers, including 0, with no decimal or fractional parts
Even numbers are divisible by 2
Odd Numbers are not divisible by 2
Palindromes have equal numbers when digits are reversed
For more math formulas, check out our Formula Dossier
What 11 concepts are covered in the Number Property Calculator?
divisora number by which another number is to be divided.evennarcissistic numbersa given number base b is a number that is the sum of its own digits each raised to the power of the number of digits.numberan arithmetical value, expressed by a word, symbol, or figure, representing a particular quantity and used in counting and making calculations and for showing order in a series or for identification. A quantity or amount.number propertyoddpalindromeA word or phrase which reads the same forwards or backwardspentagona polygon of five angles and five sidespentagonal numberA number that can be shown as a pentagonal pattern of dots.n(3n - 1)/2perfect numbera positive integer that is equal to the sum of its positive divisors, excluding the number itself.propertyan attribute, quality, or characteristic of something
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