Show numerical properties of 4
We start by listing out divisors for 4
| Divisor | Divisor Math |
|---|---|
| 1 | 4 ÷ 1 = 4 |
| 2 | 4 ÷ 2 = 2 |
Positive or Negative Number Test:
Positive Numbers > 0
Since 4 ≥ 0 and it is an integer
4 is a positive number
Whole Number Test:
Positive numbers including 0
with no decimal or fractions
Since 4 ≥ 0 and it is an integer
4 is a whole number
Prime or Composite Test:
Since 4 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
Divisor Sum = 3
Since our divisor sum of 3 < 4
4 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
| 2 = | 4 |
| 2 |
Since 2 is an integer, 4 is divisible by 2
it is an even number
This can be written as A(4) = 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
4 to binary = 100
There are 1 1's, 4 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 3 items, we cannot form a pyramid
4 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) = 4
4 is not rectangular
Rectangular number:
Automorphic (Curious) Test:
Does n2 ends with n
42 = 4 x 4 = 16
Since 16 does not end with 4
it is not automorphic (curious)
Automorphic number:
Undulating Test:
Do the digits of n alternate in the form abab
Since 4 < 100
We only perform the test on numbers > 99
Square Test:
Is there a number m such that m2 = n?
22 = 4
Since 4 is the square of 2
4 is a square
Cube Test:
Is there a number m such that m3 = n
13 = 1 and 23 = 8 ≠ 4
Therefore, 4 is not a cube
Palindrome Test:
Is the number read backwards equal to the number?
The number read backwards is 4
Since 4 is the same backwards and forwards
it is a palindrome
Palindromic Prime Test:
Is it both prime and a palindrome
From above, since 4 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 4 ≠ 1
then it is NOT repunit
Apocalyptic Power Test:
Does 2n contain the consecutive digits 666?
24 = 16
Since 24 does not have 666
4 is NOT an apocalyptic power
Pentagonal Test:
It satisfies the form:
| n(3n - 1) | |
| 2 |
Check values of 1 and 2
Using n = 2, we have:
| 2(3(2 - 1) | |
| 2 |
| 2(6 - 1) | |
| 2 |
| 2(5) | |
| 2 |
| 10 | |
| 2 |
5 ← Since this does not equal 4
this is NOT a pentagonal number
Using n = 1, we have:
| 1(3(1 - 1) | |
| 2 |
| 1(3 - 1) | |
| 2 |
| 1(2) | |
| 2 |
| 2 | |
| 2 |
1 ← Since this does not equal 4
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) = 4
Therefore 4 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 = 4
Therefore 4 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) = 4
Therefore 4 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 = 4
Therefore 4 is not nonagonal
Nonagonal number:
Tetrahedral (Pyramidal) Test:
Tetrahederal numbers satisfy the form:
| n(n + 1)(n + 2) | |
| 6 |
Using n = 2, we have:
| 2(2 + 1)(2 + 2) | |
| 6 |
| 2(3)(4) | |
| 6 |
| 24 | |
| 6 |
4 ← Since this equals 4
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
4 is a 1 digit number, so m = 1
Square sum of digitsm = 41
Square sum of digitsm = 4
Square sum of digitsm = 4
Since 4 = 4
4 is narcissistic (plus perfect)
Catalan Test:
| Cn = | 2n! |
| (n + 1)!n! |
Check values of 2 and 3
Using n = 3, we have:
| C3 = | (2 x 3)! |
| 3!(3 + 1)! |
Using our factorial lesson
| C3 = | 6! |
| 3!4! |
| C3 = | 720 |
| (6)(24) |
| C3 = | 720 |
| 144 |
C3 = 5
Since this does not equal 4
This is NOT a Catalan number
Using n = 2, we have:
| C2 = | (2 x 2)! |
| 2!(2 + 1)! |
Using our factorial lesson
| C2 = | 4! |
| 2!3! |
| C2 = | 24 |
| (2)(6) |
| C2 = | 24 |
| 12 |
C2 = 2
Since this does not equal 4
This is NOT a Catalan number
Number Properties for 4
Final Answer
Whole
Composite
Deficient
Even
Odious
Square
Palindrome
Tetrahedral (Pyramidal)
Narcissistic (Plus Perfect)
You have 2 free calculationss remaining
What is the Answer?
Whole
Composite
Deficient
Even
Odious
Square
Palindrome
Tetrahedral (Pyramidal)
Narcissistic (Plus Perfect)
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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