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 Numbers > 0
Since 35 ≥ 0 and it is an integer
35 is a positive number
Positive numbers including 0
with no decimal or fractions
Since 35 ≥ 0 and it is an integer
35 is a whole number
Since 35 has divisors other than 1 and itself
it is a composite number
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!
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
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
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
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
Does n2 ends with n
352 = 35 x 35 = 1225
Since 1225 does not end with 35
it is not automorphic (curious)
Do the digits of n alternate in the form abab
Since 35 < 100
We only perform the test on numbers > 99
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
Is there a number m such that m3 = n
33 = 27 and 43 = 64 ≠ 35
Therefore, 35 is not a cube
Is the number read backwards equal to the number?
The number read backwards is 53
Since 35 <> 53
it is not a palindrome
Is it both prime and a palindrome
From above, since 35 is not both prime and a palindrome
it is NOT a palindromic prime
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
Does 2n contain the consecutive digits 666?
235 = 34359738368
Since 235 does not have 666
35 is NOT an apocalyptic power
It satisfies the form:
n(3n - 1) | |
2 |
5(3(5 - 1) | |
2 |
5(15 - 1) | |
2 |
5(14) | |
2 |
70 | |
2 |
35 ← Since this equals 35
this is a pentagonal number
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
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
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
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
Tetrahederal numbers satisfy the form:
n(n + 1)(n + 2) | |
6 |
5(5 + 1)(5 + 2) | |
6 |
5(6)(7) | |
6 |
210 | |
6 |
35 ← Since this equals 35
This is a tetrahedral (Pyramidal)number
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 digitsm = 32 + 52
Square sum of digitsm = 9 + 25
Square sum of digitsm = 34
Since 34 <> 35
35 is NOT narcissistic (plus perfect)
Cn = | 2n! |
(n + 1)!n! |
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
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