# Numerical properties of 35

## Enter Integer

Show numerical properties of 35

We start by listing out divisors for 35
DivisorDivisor Math
135 ÷ 1 = 35
535 ÷ 5 = 7
735 ÷ 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: 1st  2nd  3rd  4th  5th  6th  7th  8th  9th  10th

## 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: 1st  2nd  3rd  4th  5th  6th  7th  8th  9th  10th

## 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: 1st  2nd  3rd  4th  5th  6th  7th  8th  9th  10th

## 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 contains 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: 1st  2nd  3rd  4th  5th  6th  7th  8th  9th  10th

## 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: 1st  2nd  3rd  4th  5th  6th  7th  8th  9th  10th

## 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: 1st  2nd  3rd  4th  5th  6th  7th  8th  9th  10th

## 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: 1st  2nd  3rd  4th  5th  6th  7th  8th  9th  10th

## 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: 1st  2nd  3rd  4th  5th  6th  7th  8th  9th  10th

## Tetrahedral (Pyramidal) Test:

Satisfies 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

## Property Summary for the number 35

·  Positive
·  Whole
·  Composite
·  Deficient
·  Odd
·  Odious
·  Pentagonal
·  Tetrahedral (Pyramidal)

Positive
Whole
Composite
Deficient
Odd
Odious
Pentagonal
Tetrahedral (Pyramidal)

### How does the Number Property Calculator work?

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?

1. Positive Numbers are greater than 0
2. Whole Numbers are positive numbers, including 0, with no decimal or fractional parts
3. Even numbers are divisible by 2
4. Odd Numbers are not divisible by 2
5. 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