Show numerical properties of 15
We start by listing out divisors for 15
Divisor | Divisor Math |
---|---|
1 | 15 ÷ 1 = 15 |
3 | 15 ÷ 3 = 5 |
5 | 15 ÷ 5 = 3 |
Positive Numbers > 0
Since 15 ≥ 0 and it is an integer
15 is a positive number
Positive numbers including 0
with no decimal or fractions
Since 15 ≥ 0 and it is an integer
15 is a whole number
Since 15 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 + 3 + 5
Divisor Sum = 9
Since our divisor sum of 9 < 15
15 is a deficient number!
A number is even if it is divisible by 2
If not divisible by 2, it is odd
7.5 = | 15 |
2 |
Since 7.5 is not an integer, 15 is not divisible by
it is an odd number
This can be written as A(15) = 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
15 to binary = 1111
There are 4 1's, 15 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 5 items, 15 forms a triangle
It is a triangular number
Is there an integer m such that n = m(m + 1)
No integer m exists such that m(m + 1) = 15
15 is not rectangular
Does n2 ends with n
152 = 15 x 15 = 225
Since 225 does not end with 15
it is not automorphic (curious)
Do the digits of n alternate in the form abab
Since 15 < 100
We only perform the test on numbers > 99
Is there a number m such that m2 = n?
32 = 9 and 42 = 16 which do not equal 15
Therefore, 15 is not a square
Is there a number m such that m3 = n
23 = 8 and 33 = 27 ≠ 15
Therefore, 15 is not a cube
Is the number read backwards equal to the number?
The number read backwards is 51
Since 15 <> 51
it is not a palindrome
Is it both prime and a palindrome
From above, since 15 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 15 ≠ 1
then it is NOT repunit
Does 2n contain the consecutive digits 666?
215 = 32768
Since 215 does not have 666
15 is NOT an apocalyptic power
It satisfies the form:
n(3n - 1) | |
2 |
4(3(4 - 1) | |
2 |
4(12 - 1) | |
2 |
4(11) | |
2 |
44 | |
2 |
22 ← Since this does not equal 15
this is NOT a pentagonal number
3(3(3 - 1) | |
2 |
3(9 - 1) | |
2 |
3(8) | |
2 |
24 | |
2 |
12 ← Since this does not equal 15
this is NOT a pentagonal number
Is there an integer m such that n = m(2m - 1)
The integer m = 3 is hexagonal
Since 3(2(3) - 1) = 15
Is there an integer m such that:
m = | n(5n - 3) |
2 |
No integer m exists such that m(5m - 3)/2 = 15
Therefore 15 is not heptagonal
Is there an integer m such that n = m(3m - 3)
No integer m exists such that m(3m - 2) = 15
Therefore 15 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 = 15
Therefore 15 is not nonagonal
Tetrahederal numbers satisfy the form:
n(n + 1)(n + 2) | |
6 |
4(4 + 1)(4 + 2) | |
6 |
4(5)(6) | |
6 |
120 | |
6 |
20 ← Since this does not equal 15
This is NOT a tetrahedral (Pyramidal) number
3(3 + 1)(3 + 2) | |
6 |
3(4)(5) | |
6 |
60 | |
6 |
10 ← Since this does not equal 15
This is NOT a tetrahedral (Pyramidal) number
Is equal to the square sum of it's m-th powers of its digits
15 is a 2 digit number, so m = 2
Square sum of digitsm = 12 + 52
Square sum of digitsm = 1 + 25
Square sum of digitsm = 26
Since 26 <> 15
15 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 15
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 15
This is NOT a Catalan number