 # Numerical properties of 100

## Enter Integer

Show numerical properties of 100

We start by listing out divisors for 100
DivisorDivisor Math
1100 ÷ 1 = 100
2100 ÷ 2 = 50
4100 ÷ 4 = 25
5100 ÷ 5 = 20
10100 ÷ 10 = 10
20100 ÷ 20 = 5
25100 ÷ 25 = 4
50100 ÷ 50 = 2

## Positive or Negative Number Test:

Positive Numbers > 0
Since 100 ≥ 0 and it is an integer
100 is a positive number

## Whole Number Test:

Positive numbers including 0
with no decimal or fractions
Since 100 ≥ 0 and it is an integer
100 is a whole number

## Prime or Composite Test:

Since 100 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 + 5 + 10 + 20 + 25 + 50
Divisor Sum = 117
Since our divisor sum of 117 > 100
100 is an abundant 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
 50  = 100 2

Since 50 is an integer, 100 is divisible by 2
it is an even number
This can be written as A(100) = 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
100 to binary = 1100100
There are 3 1's, 100 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 14 items, we cannot form a pyramid
100 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) = 100
100 is not rectangular

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

## Automorphic (Curious) Test:

Does n2 ends with n
1002 = 100 x 100 = 10000
Since 10000 does not end with 100
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
In this case, a = 1 and b = 0
In order to be undulating, Digit 1: 111 should be equal to 1
In order to be undulating, Digit 2: 000 should be equal to 0
Since our digit pattern does not alternate in our abab pattern100 is not undulating

## Square Test:

Is there a number m such that m2 = n
102 = 100
Since 100 is the square of 10
100 is a square

## Cube Test:

Is there a number m such that m3 = n
43 = 64 and 53 = 125 ≠ 100
Therefore, 100 is not a cube

## Palindrome Test:

Is the number read backwards equal to the number?
The number read backwards is 001
Since 100 <> 001
it is not a palindrome

## Palindromic Prime Test:

Is it both prime and a palindrome
From above, since 100 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 100 ≠ 1
then it is NOT repunit

## Apocalyptic Power Test:

Does 2n contains the consecutive digits 666.
2100 = 1.2676506002282E+30
Since 2100 does not have 666
100 is NOT an apocalyptic power

## Pentagonal Test:

It satisfies the form:
 n(3n - 1) 2

## Check values of 8 and 9

Using n = 9, we have:
 9(3(9 - 1) 2

 9(27 - 1) 2

 9(26) 2

 234 2

117 ← Since this does not equal 100
this is NOT a pentagonal number

Using n = 8, we have:
 8(3(8 - 1) 2

 8(24 - 1) 2

 8(23) 2

 184 2

92 ← Since this does not equal 100
this is NOT 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) = 100
Therefore 100 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 = 100
Therefore 100 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) = 100
Therefore 100 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 = 100
Therefore 100 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

## Check values of 7 and 8

Using n = 8, we have:
 8(8 + 1)(8 + 2) 6

 8(9)(10) 6

 720 6

120 ← Since this does not equal 100
This is NOT a tetrahedral (Pyramidal) number

Using n = 7, we have:
 7(7 + 1)(7 + 2) 6

 7(8)(9) 6

 504 6

84 ← Since this does not equal 100
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
100 is a 3 digit number, so m = 3
Square sum of digitsm = 13 + 03 + 03
Square sum of digitsm = 1 + 0 + 0
Square sum of digitsm = 1
Since 1 <> 100
100 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 100
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 100
This is NOT a Catalan number

## Property Summary for the number 100

·  Positive
·  Whole
·  Composite
·  Abundant
·  Even
·  Odious
·  Square

Positive
Whole
Composite
Abundant
Even
Odious
Square

### 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