Show numerical properties of -81
We start by listing out divisors for -81
Divisor | Divisor Math |
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Since -81 is less than 0
-81 is a a negative number
Since -81 is not both ≥ 0 and an integer
-81 is a not a whole number
Since -81 has divisors other than 1 and itself
it is a composite number
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 =
Divisor Sum = 0
Since our divisor sum of 0 > -81
-81 is an abundant number!
A number is even if it is divisible by 2
If not divisible by 2, it is odd
-40.5 = | -81 |
2 |
Since -40.5 is not an integer, -81 is not divisible by
it is an odd number
This can be written as A(-81) = Odd
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
There are 0 1's, -81 is an evil number
Can you stack numbers in a pyramid?
Each row above has one item less than the row before it
Using a bottom row of 0 items, we cannot form a pyramid
-81 is not triangular
Is there an integer m such that n = m(m + 1)
No integer m exists such that m(m + 1) = -81
-81 is not rectangular
Does n2 ends with n
-812 = -81 x -81 = 6561
Since 6561 does not end with -81
it is not automorphic (curious)
Do the digits of n alternate in the form abab
Since -81 < 100
We only perform the test on numbers > 99
Is there a number m such that m2 = n?
NAN2 = NAN and NAN2 = NAN which do not equal -81
Therefore, -81 is not a square
Is there a number m such that m3 = n
03 = 0 and 13 = 1 ≠ -81
Therefore, -81 is not a cube
Is the number read backwards equal to the number?
The number read backwards is 18-
Since -81 <> 18-
it is not a palindrome
Is it both prime and a palindrome
From above, since -81 is not both prime and a palindrome
it is NOT a palindromic prime
A number is repunit if every digit is equal to 1
Since there is at least one digit in -81 ≠ 1
then it is NOT repunit
Does 2n contain the consecutive digits 666?
2-81 = 4.1359030627651E-25
Since 2-81 does not have 666
-81 is NOT an apocalyptic power
It satisfies the form:
n(3n - 1) | |
2 |
1(3(1 - 1) | |
2 |
1 ← Since this does not equal -81
this is NOT a pentagonal number
0(3(0 - 1) | |
2 |
0 ← Since this does not equal -81
this is NOT a pentagonal number
Is there an integer m such that n = m(2m - 1)
No integer m exists such that m(2m - 1) = -81
Therefore -81 is not hexagonal
Is there an integer m such that:
m = | n(5n - 3) |
2 |
No integer m exists such that m(5m - 3)/2 = -81
Therefore -81 is not heptagonal
Is there an integer m such that n = m(3m - 3)
No integer m exists such that m(3m - 2) = -81
Therefore -81 is not octagonal
Is there an integer m such that:
m = | n(7n - 5) |
2 |
No integer m exists such that m(7m - 5)/2 = -81
Therefore -81 is not nonagonal
Tetrahederal numbers satisfy the form:
n(n + 1)(n + 2) | |
6 |
1(1 + 1)(1 + 2) | |
6 |
1 ← Since this does not equal -81
This is NOT a tetrahedral (Pyramidal) number
0(0 + 1)(0 + 2) | |
6 |
0 ← Since this does not equal -81
This is NOT a tetrahedral (Pyramidal) number
Is equal to the square sum of it's m-th powers of its digits
-81 is a 2 digit number, so m = 2
Square sum of digitsm = 82 + 12
Square sum of digitsm = 64 + 1
Square sum of digitsm = -65
Since -65 <> -81
-81 is NOT narcissistic (plus perfect)
Cn = | 2n! |
(n + 1)!n! |
C1 = | (2 x 1)! |
1!(1 + 1)! |
Using our factorial lesson
C1 = | 2! |
1!2! |
C1 = | 2 |
(1)(2) |
C1 = | 2 |
2 |
C1 = 1
Since this does not equal -81
This is NOT a Catalan number
C0 = | (2 x 0)! |
0!(0 + 1)! |
Using our factorial lesson
C0 = | 0! |
0!1! |
C0 = | 1 |
(1)(1) |
C0 = | 1 |
1 |
C0 = 1
Since this does not equal -81
This is NOT a Catalan number
Negative
Composite
Abundant
Odd
Evil
Negative
Composite
Abundant
Odd
Evil
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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