Numerical properties of 35

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Show numerical properties of 35

We start by listing out divisors for 35

Divisor	Divisor Math
1	35 ÷ 1 = 35
5	35 ÷ 5 = 7
7	35 ÷ 7 = 5

Positive or Negative Number Test:

Positive Numbers > 0

Since 35 ≥ 0 and it is an integer
35 is a positive number

Whole Number Test:

Positive numbers including 0
with no decimal or fractions

Since 35 ≥ 0 and it is an integer
35 is a whole number

Prime or Composite Test:

Since 35 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 + 5 + 7
Divisor Sum = 13
Since our divisor sum of 13 < 35
35 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

17.5  =	35
	2

Since 17.5 is not an integer, 35 is not divisible by
it is an odd number
This can be written as A(35) = 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
35 to binary = 100011
There are 3 1's, 35 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 8 items, we cannot form a pyramid
35 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) = 35
35 is not rectangular

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

Automorphic (Curious) Test:

Does n² ends with n
35² = 35 x 35 = 1225
Since 1225 does not end with 35
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
Since 35 < 100
We only perform the test on numbers > 99

Square Test:

Is there a number m such that m² = n
5² = 25 and 6² = 36 which do not equal 35
Therefore, 35 is not a square

Cube Test:

Is there a number m such that m³ = n
3³ = 27 and 4³ = 64 ≠ 35
Therefore, 35 is not a cube

Palindrome Test:

Is the number read backwards equal to the number?
The number read backwards is 53
Since 35 <> 53
it is not a palindrome

Palindromic Prime Test:

Is it both prime and a palindrome
From above, since 35 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 35 ≠ 1
then it is NOT repunit

Apocalyptic Power Test:

Does 2ⁿ contains the consecutive digits 666.
2³⁵ = 34359738368
Since 2³⁵ does not have 666
35 is NOT an apocalyptic power

Pentagonal Test:

It satisfies the form:

n(3n - 1)
2

Using n = 5, we have:

5(3(5 - 1)
2

5(15 - 1)
2

5(14)
2

70
2

35 ← Since this equals 35
this is 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) = 35
Therefore 35 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 = 35
Therefore 35 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) = 35
Therefore 35 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 = 35
Therefore 35 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

Using n = 5, we have:

5(5 + 1)(5 + 2)
6

5(6)(7)
6

210
6

35 ← Since this equals 35
This is a tetrahedral (Pyramidal)number

Narcissistic (Plus Perfect) Test:

Is equal to the square sum of it's m-th powers of its digits
35 is a 2 digit number, so m = 2
Square sum of digits^m = 3² + 5²
Square sum of digits^m = 9 + 25
Square sum of digits^m = 34
Since 34 <> 35
35 is NOT narcissistic (plus perfect)

Catalan Test:

Cn  =	2n!
	(n + 1)!n!

Check values of 4 and 5

Using n = 5, we have:

C5  =	(2 x 5)!
	5!(5 + 1)!

Using our factorial lesson

C5  =	10!
	5!6!

C5  =	3628800
	(120)(720)

C5  =	3628800
	86400

C₅ = 42
Since this does not equal 35
This is NOT a Catalan number

Using n = 4, we have:

C4  =	(2 x 4)!
	4!(4 + 1)!

Using our factorial lesson

C4  =	8!
	4!5!

C4  =	40320
	(24)(120)

C4  =	40320
	2880

C₄ = 14
Since this does not equal 35
This is NOT a Catalan number

Property Summary for the number 35

  ·  Positive
  ·  Whole
  ·  Composite
  ·  Deficient
  ·  Odd
  ·  Odious
  ·  Pentagonal
  ·  Tetrahedral (Pyramidal)

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Tags:

• divisor
• even
• narcissistic numbers
• number property
• number
• odd
• palindrome
• pentagon
• pentagonal number
• perfect number
• property

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