Numerical properties of 45

Show numerical properties of 45 We start by listing out divisors for 45 Since 45 0 and it is an integer45 is a positive number Since 45 0 and it is an integer45 is a whole number Since 45 has divisors other than 1 and itselfit is a composite number

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Show numerical properties of 45

We start by listing out divisors for 45

DivisorDivisor Math
145 ÷ 1 = 45
345 ÷ 3 = 15
545 ÷ 5 = 9
945 ÷ 9 = 5
1545 ÷ 15 = 3
Positive or Negative Number Test:
Positive Numbers > 0

Since 45 ≥ 0 and it is an integer
45 is a positive number

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

Since 45 ≥ 0 and it is an integer
45 is a whole number

Prime or Composite Test:

Since 45 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 + 9 + 15

Divisor Sum = 33

Since our divisor sum of 33 < 45
45 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

22.5  =  45
  2

Since 22.5 is not an integer, 45 is not divisible by
it is an odd number

This can be written as A(45) = 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

45 to binary = 101101

There are 4 1's, 45 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 9 items, 45 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) = 45
45 is not rectangular

Rectangular number:

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Automorphic (Curious) Test:

Does n2 ends with n

452 = 45 x 45 = 2025

Since 2025 does not end with 45
it is not automorphic (curious)

Automorphic number:

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Undulating Test:

Do the digits of n alternate in the form abab

Since 45 < 100
We only perform the test on numbers > 99

Square Test:

Is there a number m such that m2 = n?

62 = 36 and 72 = 49 which do not equal 45

Therefore, 45 is not a square

Cube Test:

Is there a number m such that m3 = n

33 = 27 and 43 = 64 ≠ 45

Therefore, 45 is not a cube

Palindrome Test:

Is the number read backwards equal to the number?

The number read backwards is 54

Since 45 <> 54
it is not a palindrome

Palindromic Prime Test:

Is it both prime and a palindrome

From above, since 45 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 45 ≠ 1
then it is NOT repunit

Apocalyptic Power Test:

Does 2n contain the consecutive digits 666?

245 = 35184372088832

Since 245 does not have 666
45 is NOT an apocalyptic power

Pentagonal Test:

It satisfies the form:

n(3n - 1)
2

Check values of 5 and 6
Using n = 6, we have:
6(3(6 - 1)
2

6(18 - 1)
2


51 ← Since this does not equal 45
this is NOT a pentagonal number

Using n = 5, we have:
5(3(5 - 1)
2

5(15 - 1)
2


35 ← Since this does not equal 45
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 = 5 is hexagonal
Since 5(2(5) - 1) = 45

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 = 45
Therefore 45 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) = 45
Therefore 45 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 = 45
Therefore 45 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 5 and 6
Using n = 6, we have:
6(6 + 1)(6 + 2)
6


56 ← Since this does not equal 45
This is NOT a tetrahedral (Pyramidal) number

Using n = 5, we have:
5(5 + 1)(5 + 2)
6


35 ← Since this does not equal 45
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

45 is a 2 digit number, so m = 2

Square sum of digitsm = 42 + 52

Square sum of digitsm = 16 + 25

Square sum of digitsm = 41

Since 41 <> 45
45 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 45
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 45
This is NOT a Catalan number

Number Properties for 45
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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