Show numerical properties of 35
We start by listing out divisors for 35
| Divisor | Divisor Math |
|---|---|
| 1 | 35 ÷ 1 = 35 |
| 5 | 35 ÷ 5 = 7 |
| 7 | 35 ÷ 7 = 5 |
Positive or Negative Number Test:
Positive Numbers > 0
Since 35 ≥ 0 and it is an integer
35 is a positive number
Whole Number Test:
Positive numbers including 0
with no decimal or fractions
Since 35 ≥ 0 and it is an integer
35 is a whole number
Prime or Composite Test:
Since 35 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 + 7
Divisor Sum = 13
Since our divisor sum of 13 < 35
35 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
| 17.5 = | 35 |
| 2 |
Since 17.5 is not an integer, 35 is not divisible by
it is an odd number
This can be written as A(35) = 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
35 to binary = 100011
There are 3 1's, 35 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 8 items, we cannot form a pyramid
35 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) = 35
35 is not rectangular
Rectangular number:
Automorphic (Curious) Test:
Does n2 ends with n
352 = 35 x 35 = 1225
Since 1225 does not end with 35
it is not automorphic (curious)
Automorphic number:
Undulating Test:
Do the digits of n alternate in the form abab
Since 35 < 100
We only perform the test on numbers > 99
Square Test:
Is there a number m such that m2 = n?
52 = 25 and 62 = 36 which do not equal 35
Therefore, 35 is not a square
Cube Test:
Is there a number m such that m3 = n
33 = 27 and 43 = 64 ≠ 35
Therefore, 35 is not a cube
Palindrome Test:
Is the number read backwards equal to the number?
The number read backwards is 53
Since 35 <> 53
it is not a palindrome
Palindromic Prime Test:
Is it both prime and a palindrome
From above, since 35 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 35 ≠ 1
then it is NOT repunit
Apocalyptic Power Test:
Does 2n contain the consecutive digits 666?
235 = 34359738368
Since 235 does not have 666
35 is NOT an apocalyptic power
Pentagonal Test:
It satisfies the form:
| n(3n - 1) | |
| 2 |
Using n = 5, we have:
| 5(3(5 - 1) | |
| 2 |
| 5(15 - 1) | |
| 2 |
| 5(14) | |
| 2 |
| 70 | |
| 2 |
35 ← Since this equals 35
this is 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) = 35
Therefore 35 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 = 35
Therefore 35 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) = 35
Therefore 35 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 = 35
Therefore 35 is not nonagonal
Nonagonal number:
Tetrahedral (Pyramidal) Test:
Tetrahederal numbers satisfy the form:
| n(n + 1)(n + 2) | |
| 6 |
Using n = 5, we have:
| 5(5 + 1)(5 + 2) | |
| 6 |
| 5(6)(7) | |
| 6 |
| 210 | |
| 6 |
35 ← Since this equals 35
This is a tetrahedral (Pyramidal)number
Narcissistic (Plus Perfect) Test:
Is equal to the square sum of it's m-th powers of its digits
35 is a 2 digit number, so m = 2
Square sum of digitsm = 32 + 52
Square sum of digitsm = 9 + 25
Square sum of digitsm = 34
Since 34 <> 35
35 is NOT narcissistic (plus perfect)
Catalan Test:
| Cn = | 2n! |
| (n + 1)!n! |
Check values of 4 and 5
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 35
This is NOT a Catalan number
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 35
This is NOT a Catalan number
Number Properties for 35
Final Answer
Whole
Composite
Deficient
Odd
Odious
Pentagonal
Tetrahedral (Pyramidal)
You have 2 free calculationss remaining
What is the Answer?
Whole
Composite
Deficient
Odd
Odious
Pentagonal
Tetrahedral (Pyramidal)
How does the Number Property Calculator work?
* 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?
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
Example calculations for the Number Property Calculator
Number Property Calculator Video
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