Show numerical properties of 30
We start by listing out divisors for 30
Divisor | Divisor Math |
---|---|
1 | 30 ÷ 1 = 30 |
2 | 30 ÷ 2 = 15 |
3 | 30 ÷ 3 = 10 |
5 | 30 ÷ 5 = 6 |
6 | 30 ÷ 6 = 5 |
10 | 30 ÷ 10 = 3 |
15 | 30 ÷ 15 = 2 |
Positive Numbers > 0
Since 30 ≥ 0 and it is an integer
30 is a positive number
Positive numbers including 0
with no decimal or fractions
Since 30 ≥ 0 and it is an integer
30 is a whole number
Since 30 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 + 2 + 3 + 5 + 6 + 10 + 15
Divisor Sum = 42
Since our divisor sum of 42 > 30
30 is an abundant number!
A number is even if it is divisible by 2
If not divisible by 2, it is odd
15 = | 30 |
2 |
Since 15 is an integer, 30 is divisible by 2
it is an even number
This can be written as A(30) = Even
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
30 to binary = 11110
There are 4 1's, 30 is an evil 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
30 is not triangular
Is there an integer m such that n = m(m + 1)
The integer m = 5 satisifes our rectangular number property.
5(5 + 1) = 30
Does n2 ends with n
302 = 30 x 30 = 900
Since 900 does not end with 30
it is not automorphic (curious)
Do the digits of n alternate in the form abab
Since 30 < 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 30
Therefore, 30 is not a square
Is there a number m such that m3 = n
33 = 27 and 43 = 64 ≠ 30
Therefore, 30 is not a cube
Is the number read backwards equal to the number?
The number read backwards is 03
Since 30 <> 03
it is not a palindrome
Is it both prime and a palindrome
From above, since 30 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 30 ≠ 1
then it is NOT repunit
Does 2n contain the consecutive digits 666?
230 = 1073741824
Since 230 does not have 666
30 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 does not equal 30
this is NOT a pentagonal number
4(3(4 - 1) | |
2 |
4(12 - 1) | |
2 |
4(11) | |
2 |
44 | |
2 |
22 ← Since this does not equal 30
this is NOT a pentagonal number
Is there an integer m such that n = m(2m - 1)
No integer m exists such that m(2m - 1) = 30
Therefore 30 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 = 30
Therefore 30 is not heptagonal
Is there an integer m such that n = m(3m - 3)
No integer m exists such that m(3m - 2) = 30
Therefore 30 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 = 30
Therefore 30 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 does not equal 30
This is NOT a tetrahedral (Pyramidal) number
4(4 + 1)(4 + 2) | |
6 |
4(5)(6) | |
6 |
120 | |
6 |
20 ← Since this does not equal 30
This is NOT a tetrahedral (Pyramidal) number
Is equal to the square sum of it's m-th powers of its digits
30 is a 2 digit number, so m = 2
Square sum of digitsm = 32 + 02
Square sum of digitsm = 9 + 0
Square sum of digitsm = 9
Since 9 <> 30
30 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 30
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 30
This is NOT a Catalan number