Numerical properties of 85
Show numerical properties of 85
We start by listing out divisors for 85
| Divisor | Divisor Math |
|---|---|
| 1 | 85 ÷ 1 = 85 |
| 5 | 85 ÷ 5 = 17 |
| 17 | 85 ÷ 17 = 5 |
Positive or Negative Number Test:
Positive Numbers > 0
Since 85 ≥ 0 and it is an integer
85 is a positive number
Whole Number Test:
Positive numbers including 0
with no decimal or fractions
Since 85 ≥ 0 and it is an integer
85 is a whole number
Prime or Composite Test:
Since 85 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 + 5 + 17
Divisor Sum = 23
Since our divisor sum of 23 < 85
85 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
| 42.5 = | 85 |
| 2 |
Since 42.5 is not an integer, 85 is not divisible by
it is an odd number
This can be written as A(85) = Odd
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
85 to binary = 1010101
There are 4 1's, 85 is an evil 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 13 items, we cannot form a pyramid
85 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) = 85
85 is not rectangular
Rectangular number:
Automorphic (Curious) Test:
Does n2 ends with n
852 = 85 x 85 = 7225
Since 7225 does not end with 85
it is not automorphic (curious)
Automorphic number:
Undulating Test:
Do the digits of n alternate in the form abab
Since 85 < 100
We only perform the test on numbers > 99
Square Test:
Is there a number m such that m2 = n?
92 = 81 and 102 = 100 which do not equal 85
Therefore, 85 is not a square
Cube Test:
Is there a number m such that m3 = n
43 = 64 and 53 = 125 ≠ 85
Therefore, 85 is not a cube
Palindrome Test:
Is the number read backwards equal to the number?
The number read backwards is 58
Since 85 <> 58
it is not a palindrome
Palindromic Prime Test:
Is it both prime and a palindrome
From above, since 85 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 85 ≠ 1
then it is NOT repunit
Apocalyptic Power Test:
Does 2n contain the consecutive digits 666?
285 = 3.8685626227668E+25
Since 285 does not have 666
85 is NOT an apocalyptic power
Pentagonal Test:
It satisfies the form:
| n(3n - 1) | |
| 2 |
Check values of 7 and 8
Using n = 8, we have:
| 8(3(8 - 1) | |
| 2 |
| 8(24 - 1) | |
| 2 |
92 ← Since this does not equal 85
this is NOT a pentagonal number
Using n = 7, we have:
| 7(3(7 - 1) | |
| 2 |
| 7(21 - 1) | |
| 2 |
70 ← Since this does not equal 85
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) = 85
Therefore 85 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 = 85
Therefore 85 is not heptagonal
Heptagonal number:
Octagonal Test:
Is there an integer m such that n = m(3m - 3)
No integer m exists such that m(3m - 2) = 85
Therefore 85 is not octagonal
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 = 85
Therefore 85 is not nonagonal
Nonagonal number:
Tetrahedral (Pyramidal) Test:
Tetrahederal numbers satisfy the form:
| n(n + 1)(n + 2) | |
| 6 |
Check values of 7 and 8
Using n = 8, we have:
| 8(8 + 1)(8 + 2) | |
| 6 |
120 ← Since this does not equal 85
This is NOT a tetrahedral (Pyramidal) number
Using n = 7, we have:
| 7(7 + 1)(7 + 2) | |
| 6 |
84 ← Since this does not equal 85
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
85 is a 2 digit number, so m = 2
Square sum of digitsm = 82 + 52
Square sum of digitsm = 64 + 25
Square sum of digitsm = 89
Since 89 <> 85
85 is NOT narcissistic (plus perfect)
Catalan Test:
| Cn = | 2n! |
| (n + 1)!n! |
Check values of 5 and 6
Using n = 6, we have:
| C6 = | (2 x 6)! |
| 6!(6 + 1)! |
Using our factorial lesson
| C6 = | 12! |
| 6!7! |
| C6 = | 479001600 |
| (720)(5040) |
| C6 = | 479001600 |
| 3628800 |
C6 = 132
Since this does not equal 85
This is NOT a Catalan number
Using n = 5, we have:
| C5 = | (2 x 5)! |
| 5!(5 + 1)! |
Using our factorial lesson
| C5 = | 10! |
| 5!6! |
| C5 = | 3628800 |
| (120)(720) |
| C5 = | 3628800 |
| 86400 |
C5 = 42
Since this does not equal 85
This is NOT a Catalan number
Number Properties for 85
Final Answer
Positive
Whole
Composite
Deficient
Odd
Evil
You have 1 free calculations remaining
What is the Answer?
Positive
Whole
Composite
Deficient
Odd
Evil
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
This calculator has 1 input.
What 5 formulas are used for the Number Property Calculator?
Positive Numbers are greater than 0
Whole 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?
- divisor
- a number by which another number is to be divided.
- even
- narcissistic numbers
- a 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.
- number
- an 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 property
- odd
- palindrome
- A word or phrase which reads the same forwards or backwards
- pentagon
- a polygon of five angles and five sides
- pentagonal number
- A number that can be shown as a pentagonal pattern of dots.
n(3n - 1)/2 - perfect number
- a positive integer that is equal to the sum of its positive divisors, excluding the number itself.
- property
- an attribute, quality, or characteristic of something
