Show numerical properties of 45
We start by listing out divisors for 45
Divisor | Divisor Math |
---|---|
1 | 45 ÷ 1 = 45 |
3 | 45 ÷ 3 = 15 |
5 | 45 ÷ 5 = 9 |
9 | 45 ÷ 9 = 5 |
15 | 45 ÷ 15 = 3 |
Positive Numbers > 0
Since 45 ≥ 0 and it is an integer
45 is a positive number
Positive numbers including 0
with no decimal or fractions
Since 45 ≥ 0 and it is an integer
45 is a whole number
Since 45 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 + 9 + 15
Divisor Sum = 33
Since our divisor sum of 33 < 45
45 is a deficient number!
A number is even if it is divisible by 2
If not divisible by 2, it is odd
22.5 = | 45 |
2 |
Since 22.5 is not an integer, 45 is not divisible by
it is an odd number
This can be written as A(45) = 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
45 to binary = 101101
There are 4 1's, 45 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 9 items, 45 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) = 45
45 is not rectangular
Does n2 ends with n
452 = 45 x 45 = 2025
Since 2025 does not end with 45
it is not automorphic (curious)
Do the digits of n alternate in the form abab
Since 45 < 100
We only perform the test on numbers > 99
Is there a number m such that m2 = n?
62 = 36 and 72 = 49 which do not equal 45
Therefore, 45 is not a square
Is there a number m such that m3 = n
33 = 27 and 43 = 64 ≠ 45
Therefore, 45 is not a cube
Is the number read backwards equal to the number?
The number read backwards is 54
Since 45 <> 54
it is not a palindrome
Is it both prime and a palindrome
From above, since 45 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 45 ≠ 1
then it is NOT repunit
Does 2n contain the consecutive digits 666?
245 = 35184372088832
Since 245 does not have 666
45 is NOT an apocalyptic power
It satisfies the form:
n(3n - 1) | |
2 |
6(3(6 - 1) | |
2 |
6(18 - 1) | |
2 |
6(17) | |
2 |
102 | |
2 |
51 ← Since this does not equal 45
this is NOT a pentagonal number
5(3(5 - 1) | |
2 |
5(15 - 1) | |
2 |
5(14) | |
2 |
70 | |
2 |
35 ← Since this does not equal 45
this is NOT a pentagonal number
Is there an integer m such that n = m(2m - 1)
The integer m = 5 is hexagonal
Since 5(2(5) - 1) = 45
Is there an integer m such that:
m = | n(5n - 3) |
2 |
No integer m exists such that m(5m - 3)/2 = 45
Therefore 45 is not heptagonal
Is there an integer m such that n = m(3m - 3)
No integer m exists such that m(3m - 2) = 45
Therefore 45 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 = 45
Therefore 45 is not nonagonal
Tetrahederal numbers satisfy the form:
n(n + 1)(n + 2) | |
6 |
6(6 + 1)(6 + 2) | |
6 |
6(7)(8) | |
6 |
336 | |
6 |
56 ← Since this does not equal 45
This is NOT a tetrahedral (Pyramidal) number
5(5 + 1)(5 + 2) | |
6 |
5(6)(7) | |
6 |
210 | |
6 |
35 ← Since this does not equal 45
This is NOT a tetrahedral (Pyramidal) number
Is equal to the square sum of it's m-th powers of its digits
45 is a 2 digit number, so m = 2
Square sum of digitsm = 42 + 52
Square sum of digitsm = 16 + 25
Square sum of digitsm = 41
Since 41 <> 45
45 is NOT narcissistic (plus perfect)
Cn = | 2n! |
(n + 1)!n! |
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 45
This is NOT a Catalan number
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 45
This is NOT a Catalan number