Show numerical properties of 191
We start by listing out divisors for 191
| Divisor | Divisor Math |
|---|---|
| 1 | 191 ÷ 1 = 191 |
Positive or Negative Number Test:
Positive Numbers > 0Since 191 ≥ 0 and it is an integer
191 is a positive number
Whole Number Test:
Positive numbers including 0with 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
Triangular number:
Rectangular Test:
Is there an integer m such that n = m(m + 1)
No integer m exists such that m(m + 1) = 191
191 is not rectangular
Rectangular number:
Automorphic (Curious) Test:
Does n2 ends with n
1912 = 191 x 191 = 36481
Since 36481 does not end with 191
it is not automorphic (curious)
Automorphic number:
Undulating Test:
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 contain 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 |
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 |
176 ← Since this does not equal 191
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) = 191
Therefore 191 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 = 191
Therefore 191 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) = 191
Therefore 191 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 = 191
Therefore 191 is not nonagonal
Nonagonal number:
Tetrahedral (Pyramidal) Test:
Tetrahederal numbers satisfy the form:
| n(n + 1)(n + 2) | |
| 6 |
Check values of 9 and 10
Using n = 10, we have:
| 10(10 + 1)(10 + 2) | |
| 6 |
| 10(11)(12) | |
| 6 |
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 |
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)
Catalan Test:
| Cn = | 2n! |
| (n + 1)!n! |
Check values of 6 and 7
Using n = 7, we have:
| C7 = | (2 x 7)! |
| 7!(7 + 1)! |
Using our factorial lesson
| C7 = | 14! |
| 7!8! |
| C7 = | 87178291200 |
| (5040)(40320) |
| C7 = | 87178291200 |
| 203212800 |
C7 = 429
Since this does not equal 191
This is NOT a Catalan number
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 191
This is NOT a Catalan number
Number Properties for 191
Final Answer
Positive
Whole
Prime
Deficient
Odd
Odious
Undulating
Palindrome
Palindromic Prime
You have 1 free calculations remaining
What is the Answer?
Positive
Whole
Prime
Deficient
Odd
Odious
Undulating
Palindrome
Palindromic Prime
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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