Since 191 ≥ 0 and it is an integer 191 is a positive number
Whole Number Test:
Positive numbers including 0 with no decimal or fractions
Since 191 ≥ 0 and it is an integer 191 is a whole number
Prime or Composite Test:
Since 191 is only divisible by 1 and itself it is a prime 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 Since our divisor sum of 1 < 191 191 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
95.5 =
191
2
Since 95.5 is not an integer, 191 is not divisible by it is an odd number This can be written as A(191) = 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 191 to binary = 10111111 There are 7 1's, 191 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 20 items, we cannot form a pyramid 191 is not triangular
Do the digits of n alternate in the form abab In this case, a = 1 and b = 9 In order to be undulating, Digit 1: 111 should be equal to 1 In order to be undulating, Digit 2: 999 should be equal to 9 In order to be undulating, Digit 3: 111 should be equal to 1 Since all 3 digits form our abab undulation pattern 191 is undulating
Square Test:
Is there a number m such that m2 = n 132 = 169 and 142 = 196 which do not equal 191 Therefore, 191 is not a square
Cube Test:
Is there a number m such that m3 = n 53 = 125 and 63 = 216 ≠ 191 Therefore, 191 is not a cube
Palindrome Test:
Is the number read backwards equal to the number? The number read backwards is 191 Since 191 is the same backwards and forwards it is a palindrome
Palindromic Prime Test:
Is it both prime and a palindrome From above, since 191 is both prime and a palindrome it is a palindromic prime
Repunit Test:
A number is repunit if every digit is equal to 1 Since there is at least one digit in 191 ≠ 1 then it is NOT repunit
Apocalyptic Power Test:
Does 2n contains the consecutive digits 666. 2191 = 3.1385508676933E+57 Since 2191 does not have 666 191 is NOT an apocalyptic power
Pentagonal Test:
It satisfies the form:
n(3n - 1)
2
Check values of 11 and 12
Using n = 12, we have:
12(3(12 - 1)
2
12(36 - 1)
2
12(35)
2
420
2
210 ← Since this does not equal 191 this is NOT a pentagonal number
Using n = 11, we have:
11(3(11 - 1)
2
11(33 - 1)
2
11(32)
2
352
2
176 ← Since this does not equal 191 this is NOT a pentagonal number
220 ← Since this does not equal 191 This is NOT a tetrahedral (Pyramidal) number
Using n = 9, we have:
9(9 + 1)(9 + 2)
6
9(10)(11)
6
990
6
165 ← Since this does not equal 191 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 191 is a 3 digit number, so m = 3 Square sum of digitsm = 13 + 93 + 13 Square sum of digitsm = 1 + 729 + 1 Square sum of digitsm = 731 Since 731 <> 191 191 is NOT narcissistic (plus perfect)
C6 = 132 Since this does not equal 191 This is NOT a Catalan number
Property Summary for the number 191
· Positive · Whole · Prime · Deficient · Odd · Odious · Undulating · Palindrome · Palindromic Prime
What is the Answer?
Positive Whole Prime Deficient Odd Odious Undulating Palindrome Palindromic Prime
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?
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?
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
Example calculations for the Number Property Calculator
