Numerical properties of 15

Show numerical properties of 15 We start by listing out divisors for 15 Since 15 0 and it is an integer15 is a positive number Since 15 0 and it is an integer15 is a whole number Since 15 has divisors other than 1 and itselfit is a composite number

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Show numerical properties of 15

We start by listing out divisors for 15

DivisorDivisor Math
115 ÷ 1 = 15
315 ÷ 3 = 5
515 ÷ 5 = 3
Positive or Negative Number Test:
Positive Numbers > 0

Since 15 ≥ 0 and it is an integer
15 is a positive number

Whole Number Test:
Positive numbers including 0
with no decimal or fractions

Since 15 ≥ 0 and it is an integer
15 is a whole number

Prime or Composite Test:

Since 15 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 + 3 + 5

Divisor Sum = 9

Since our divisor sum of 9 < 15
15 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

7.5  =  15
  2

Since 7.5 is not an integer, 15 is not divisible by
it is an odd number

This can be written as A(15) = 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

15 to binary = 1111

There are 4 1's, 15 is an evil 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 5 items, 15 forms a triangle
It is a triangular number

Triangular number:

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Rectangular Test:

Is there an integer m such that n = m(m + 1)

No integer m exists such that m(m + 1) = 15
15 is not rectangular

Rectangular number:

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Automorphic (Curious) Test:

Does n2 ends with n

152 = 15 x 15 = 225

Since 225 does not end with 15
it is not automorphic (curious)

Automorphic number:

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Undulating Test:

Do the digits of n alternate in the form abab

Since 15 < 100
We only perform the test on numbers > 99

Square Test:

Is there a number m such that m2 = n?

32 = 9 and 42 = 16 which do not equal 15

Therefore, 15 is not a square

Cube Test:

Is there a number m such that m3 = n

23 = 8 and 33 = 27 ≠ 15

Therefore, 15 is not a cube

Palindrome Test:

Is the number read backwards equal to the number?

The number read backwards is 51

Since 15 <> 51
it is not a palindrome

Palindromic Prime Test:

Is it both prime and a palindrome

From above, since 15 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 15 ≠ 1
then it is NOT repunit

Apocalyptic Power Test:

Does 2n contain the consecutive digits 666?

215 = 32768

Since 215 does not have 666
15 is NOT an apocalyptic power

Pentagonal Test:

It satisfies the form:

n(3n - 1)
2

Check values of 3 and 4
Using n = 4, we have:
4(3(4 - 1)
2

4(12 - 1)
2


22 ← Since this does not equal 15
this is NOT a pentagonal number

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



12 ← Since this does not equal 15
this is NOT a pentagonal number

Pentagonal number:

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Hexagonal Test:

Is there an integer m such that n = m(2m - 1)

The integer m = 3 is hexagonal
Since 3(2(3) - 1) = 15

Hexagonal number:

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Heptagonal Test:

Is there an integer m such that:

m  =  n(5n - 3)
  2

No integer m exists such that m(5m - 3)/2 = 15
Therefore 15 is not heptagonal

Heptagonal number:

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Octagonal Test:

Is there an integer m such that n = m(3m - 3)

No integer m exists such that m(3m - 2) = 15
Therefore 15 is not octagonal

Octagonal number:

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Nonagonal Test:

Is there an integer m such that:

m  =  n(7n - 5)
  2

No integer m exists such that m(7m - 5)/2 = 15
Therefore 15 is not nonagonal

Nonagonal number:

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Tetrahedral (Pyramidal) Test:

Tetrahederal numbers satisfy the form:

n(n + 1)(n + 2)
6

Check values of 3 and 4
Using n = 4, we have:
4(4 + 1)(4 + 2)
6


20 ← Since this does not equal 15
This is NOT a tetrahedral (Pyramidal) number

Using n = 3, we have:
3(3 + 1)(3 + 2)
6


10 ← Since this does not equal 15
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

15 is a 2 digit number, so m = 2

Square sum of digitsm = 12 + 52

Square sum of digitsm = 1 + 25

Square sum of digitsm = 26

Since 26 <> 15
15 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 15
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 15
This is NOT a Catalan number

Number Properties for 15
Final Answer

Positive
Whole
Composite
Deficient
Odd
Evil
Triangular
Hexagonal

You have 1 free calculations remaining


What is the Answer?

Positive
Whole
Composite
Deficient
Odd
Evil
Triangular
Hexagonal

How does the Number Property Calculator work?

Free Number Property Calculator - 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?

Positive Numbers are greater than 0
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?

divisora number by which another number is to be divided.evennarcissistic numbersa 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.numberan 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 propertyoddpalindromeA word or phrase which reads the same forwards or backwardspentagona polygon of five angles and five sidespentagonal numberA number that can be shown as a pentagonal pattern of dots.
n(3n - 1)/2perfect numbera positive integer that is equal to the sum of its positive divisors, excluding the number itself.propertyan attribute, quality, or characteristic of something

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