Numerical properties of 4

Enter Integer

Show numerical properties of 4

We start by listing out divisors for 4
DivisorDivisor Math
14 ÷ 1 = 4
24 ÷ 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: 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) = 4
4 is not rectangular

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

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

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 contains 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: 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) = 4
Therefore 4 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 = 4
Therefore 4 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) = 4
Therefore 4 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 = 4
Therefore 4 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 = 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

Property Summary for the number 4

·  Positive
·  Whole
·  Composite
·  Deficient
·  Even
·  Odious
·  Square
·  Palindrome
·  Tetrahedral (Pyramidal)
·  Narcissistic (Plus Perfect)

Positive
Whole
Composite
Deficient
Even
Odious
Square
Palindrome
Tetrahedral (Pyramidal)
Narcissistic (Plus Perfect)

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