Numerical properties of 72
Show numerical properties of 72
We start by listing out divisors for 72
| Divisor | Divisor Math |
|---|---|
| 1 | 72 ÷ 1 = 72 |
| 2 | 72 ÷ 2 = 36 |
| 3 | 72 ÷ 3 = 24 |
| 4 | 72 ÷ 4 = 18 |
| 6 | 72 ÷ 6 = 12 |
| 8 | 72 ÷ 8 = 9 |
| 9 | 72 ÷ 9 = 8 |
| 12 | 72 ÷ 12 = 6 |
| 18 | 72 ÷ 18 = 4 |
| 24 | 72 ÷ 24 = 3 |
| 36 | 72 ÷ 36 = 2 |
Positive or Negative Number Test:
Positive Numbers > 0Since 72 ≥ 0 and it is an integer
72 is a positive number
Whole Number Test:
Positive numbers including 0with no decimal or fractions
Since 72 ≥ 0 and it is an integer
72 is a whole number
Prime or Composite Test:
Since 72 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 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 24 + 36
Divisor Sum = 123
Since our divisor sum of 123 > 72
72 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
| 36 = | 72 |
| 2 |
Since 36 is an integer, 72 is divisible by 2
it is an even number
This can be written as A(72) = 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
72 to binary = 1001000
There are 2 1's, 72 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 12 items, we cannot form a pyramid
72 is not triangular
Triangular number:
Rectangular Test:
Is there an integer m such that n = m(m + 1)
The integer m = 8 satisifes our rectangular number property.
8(8 + 1) = 72
Rectangular number:
Automorphic (Curious) Test:
Does n2 ends with n
722 = 72 x 72 = 5184
Since 5184 does not end with 72
it is not automorphic (curious)
Automorphic number:
Undulating Test:
Do the digits of n alternate in the form abab
Since 72 < 100
We only perform the test on numbers > 99
Square Test:
Is there a number m such that m2 = n?
82 = 64 and 92 = 81 which do not equal 72
Therefore, 72 is not a square
Cube Test:
Is there a number m such that m3 = n
43 = 64 and 53 = 125 ≠ 72
Therefore, 72 is not a cube
Palindrome Test:
Is the number read backwards equal to the number?
The number read backwards is 27
Since 72 <> 27
it is not a palindrome
Palindromic Prime Test:
Is it both prime and a palindrome
From above, since 72 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 72 ≠ 1
then it is NOT repunit
Apocalyptic Power Test:
Does 2n contain the consecutive digits 666?
272 = 4.7223664828696E+21
Since 272 does not have 666
72 is NOT an apocalyptic power
Pentagonal Test:
It satisfies the form:
| n(3n - 1) | |
| 2 |
Check values of 7 and 8
Using n = 8, we have:
| 8(3(8 - 1) | |
| 2 |
| 8(24 - 1) | |
| 2 |
92 ← Since this does not equal 72
this is NOT a pentagonal number
Using n = 7, we have:
| 7(3(7 - 1) | |
| 2 |
| 7(21 - 1) | |
| 2 |
70 ← Since this does not equal 72
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) = 72
Therefore 72 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 = 72
Therefore 72 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) = 72
Therefore 72 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 = 72
Therefore 72 is not nonagonal
Nonagonal number:
Tetrahedral (Pyramidal) Test:
Tetrahederal numbers satisfy the form:
| n(n + 1)(n + 2) | |
| 6 |
Check values of 6 and 7
Using n = 7, we have:
| 7(7 + 1)(7 + 2) | |
| 6 |
84 ← Since this does not equal 72
This is NOT a tetrahedral (Pyramidal) number
Using n = 6, we have:
| 6(6 + 1)(6 + 2) | |
| 6 |
56 ← Since this does not equal 72
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
72 is a 2 digit number, so m = 2
Square sum of digitsm = 72 + 22
Square sum of digitsm = 49 + 4
Square sum of digitsm = 53
Since 53 <> 72
72 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 72
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 72
This is NOT a Catalan number
Number Properties for 72
Final Answer
Positive
Whole
Composite
Abundant
Even
Evil
Rectangular
You have 1 free calculations remaining
What is the Answer?
Positive
Whole
Composite
Abundant
Even
Evil
Rectangular
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
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What 5 formulas are used for the Number Property Calculator?
Positive Numbers are greater than 0Whole 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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