Since 72 ≥ 0 and it is an integer 72 is a positive number
Whole Number Test:
Positive numbers including 0 with 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
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
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
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
84 ← Since this does not equal 72 This is NOT a tetrahedral (Pyramidal) number
Using n = 6, we have:
6(6 + 1)(6 + 2)
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)
Positive Whole Composite Abundant Even Evil Rectangular
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
* Tetrahedral (Pyramidal)
* Narcissistic (Plus Perfect)
* 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
What 11 concepts are covered in the Number Property Calculator?
a number by which another number is to be divided.
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.
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.
A word or phrase which reads the same forwards or backwards
a polygon of five angles and five sides
A number that can be shown as a pentagonal pattern of dots. n(3n - 1)/2
a positive integer that is equal to the sum of its positive divisors, excluding the number itself.
an attribute, quality, or characteristic of something
Example calculations for the Number Property Calculator