Numerical properties of 248

Publish date: 2024-05-21
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Show numerical properties of 248

We start by listing out divisors for 248

DivisorDivisor Math
1248 ÷ 1 = 248
2248 ÷ 2 = 124
4248 ÷ 4 = 62
8248 ÷ 8 = 31
31248 ÷ 31 = 8
62248 ÷ 62 = 4
124248 ÷ 124 = 2
Positive or Negative Number Test:
Positive Numbers > 0

Since 248 ≥ 0 and it is an integer
248 is a positive number

Whole Number Test:
Positive numbers including 0
with no decimal or fractions

Since 248 ≥ 0 and it is an integer
248 is a whole number

Prime or Composite Test:

Since 248 has divisors other than 1 and itself
it is a composite 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 + 2 + 4 + 8 + 31 + 62 + 124

Divisor Sum = 232

Since our divisor sum of 232 < 248
248 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

124  =  248
  2

Since 124 is an integer, 248 is divisible by 2
it is an even number

This can be written as A(248) = Even

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

248 to binary = 11111000

There are 5 1's, 248 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 22 items, we cannot form a pyramid
248 is not triangular

Triangular number:

1st  

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Rectangular Test:

Is there an integer m such that n = m(m + 1)

No integer m exists such that m(m + 1) = 248
248 is not rectangular

Rectangular number:

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Automorphic (Curious) Test:

Does n2 ends with n

2482 = 248 x 248 = 61504

Since 61504 does not end with 248
it is not automorphic (curious)

Automorphic number:

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Undulating Test:

Do the digits of n alternate in the form abab

In this case, a = 2 and b = 4

In order to be undulating, Digit 1: 222 should be equal to 2

In order to be undulating, Digit 2: 444 should be equal to 4

Since our digit pattern does not alternate in our abab pattern248 is not undulating

Square Test:

Is there a number m such that m2 = n?

152 = 225 and 162 = 256 which do not equal 248

Therefore, 248 is not a square

Cube Test:

Is there a number m such that m3 = n

63 = 216 and 73 = 343 ≠ 248

Therefore, 248 is not a cube

Palindrome Test:

Is the number read backwards equal to the number?

The number read backwards is 842

Since 248 <> 842
it is not a palindrome

Palindromic Prime Test:

Is it both prime and a palindrome

From above, since 248 is not both prime and a palindrome
it is NOT a palindromic prime

Repunit Test:

A number is repunit if every digit is equal to 1

Since there is at least one digit in 248 ≠ 1
then it is NOT repunit

Apocalyptic Power Test:

Does 2n contain the consecutive digits 666?

2248 = 4.5231284858327E+74

Since 2248 does not have 666
248 is NOT an apocalyptic power

Pentagonal Test:

It satisfies the form:

n(3n - 1)
2

Check values of 13 and 14
Using n = 14, we have:
14(3(14 - 1)
2

14(42 - 1)
2


287 ← Since this does not equal 248
this is NOT a pentagonal number

Using n = 13, we have:
13(3(13 - 1)
2

13(39 - 1)
2


247 ← Since this does not equal 248
this is NOT a pentagonal number

Pentagonal number:

1st  

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Hexagonal Test:

Is there an integer m such that n = m(2m - 1)

No integer m exists such that m(2m - 1) = 248
Therefore 248 is not hexagonal

Hexagonal number:

1st  

2nd  

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Heptagonal Test:

Is there an integer m such that:

m  =  n(5n - 3)
  2

No integer m exists such that m(5m - 3)/2 = 248
Therefore 248 is not heptagonal

Heptagonal number:

1st  

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Octagonal Test:

Is there an integer m such that n = m(3m - 3)

No integer m exists such that m(3m - 2) = 248
Therefore 248 is not octagonal

Octagonal number:

1st  

2nd  

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Nonagonal Test:

Is there an integer m such that:

m  =  n(7n - 5)
  2

No integer m exists such that m(7m - 5)/2 = 248
Therefore 248 is not nonagonal

Nonagonal number:

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Tetrahedral (Pyramidal) Test:

Tetrahederal numbers satisfy the form:

n(n + 1)(n + 2)
6

Check values of 10 and 11
Using n = 11, we have:
11(11 + 1)(11 + 2)
6

11(12)(13)
6

286 ← Since this does not equal 248
This is NOT a tetrahedral (Pyramidal) number

Using n = 10, we have:
10(10 + 1)(10 + 2)
6

10(11)(12)
6

220 ← Since this does not equal 248
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

248 is a 3 digit number, so m = 3

Square sum of digitsm = 23 + 43 + 83

Square sum of digitsm = 8 + 64 + 512

Square sum of digitsm = 584

Since 584 <> 248
248 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 248
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 248
This is NOT a Catalan number

Number Properties for 248
Final Answer

Positive
Whole
Composite
Deficient
Even
Odious

You have 1 free calculations remaining


What is the Answer?

Positive
Whole
Composite
Deficient
Even
Odious

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 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

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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