Show numerical properties of 100
We start by listing out divisors for 100
| Divisor | Divisor Math |
|---|---|
| 1 | 100 ÷ 1 = 100 |
| 2 | 100 ÷ 2 = 50 |
| 4 | 100 ÷ 4 = 25 |
| 5 | 100 ÷ 5 = 20 |
| 10 | 100 ÷ 10 = 10 |
| 20 | 100 ÷ 20 = 5 |
| 25 | 100 ÷ 25 = 4 |
| 50 | 100 ÷ 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:
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:
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:
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 contain 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:
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:
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:
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:
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:
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 |
| 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
Number Properties for 100
Final Answer
Whole
Composite
Abundant
Even
Odious
Square
You have 2 free calculationss remaining
What is the Answer?
Whole
Composite
Abundant
Even
Odious
Square
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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