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 > 0
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
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 |
| 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
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 |
| 1320 | |
| 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 |
| 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)
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
Whole
Prime
Deficient
Odd
Odious
Undulating
Palindrome
Palindromic Prime
You have 2 free calculationss remaining
What is the Answer?
Whole
Prime
Deficient
Odd
Odious
Undulating
Palindrome
Palindromic Prime
How does the Number Property Calculator work?
* 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?
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?
- 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
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