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


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?

  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

Example calculations for the Number Property Calculator

  1. 30 as a unique number
  2. 45 as a composite number
  3. numerical properties of 100
  4. properties of 35
  5. tell me about 72
  6. A(4)

Number Property Calculator Video


Tags:



Add This Calculator To Your Website