 # Numerical properties of 191

## Enter Integer

Show numerical properties of 191

We start by listing out divisors for 191
DivisorDivisor Math
1191 ÷ 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: 1st  2nd  3rd  4th  5th  6th  7th  8th  9th  10th

## 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: 1st  2nd  3rd  4th  5th  6th  7th  8th  9th  10th

## 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: 1st  2nd  3rd  4th  5th  6th  7th  8th  9th  10th

## 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 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

Pentagonal number: 1st  2nd  3rd  4th  5th  6th  7th  8th  9th  10th

## 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: 1st  2nd  3rd  4th  5th  6th  7th  8th  9th  10th

## 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: 1st  2nd  3rd  4th  5th  6th  7th  8th  9th  10th

## 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: 1st  2nd  3rd  4th  5th  6th  7th  8th  9th  10th

## 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: 1st  2nd  3rd  4th  5th  6th  7th  8th  9th  10th

## Tetrahedral (Pyramidal) Test:

Satisfies 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

## Property Summary for the number 191

·  Positive
·  Whole
·  Prime
·  Deficient
·  Odd
·  Odious
·  Undulating
·  Palindrome
·  Palindromic Prime

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?

1. Positive Numbers are greater than 0
2. Whole Numbers are positive numbers, including 0, with no decimal or fractional parts
3. Even numbers are divisible by 2
4. Odd Numbers are not divisible by 2
5. 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