Show numerical properties of 72
We start by listing out divisors for 72
Divisor | Divisor Math |
---|---|
1 | 72 ÷ 1 = 72 |
2 | 72 ÷ 2 = 36 |
3 | 72 ÷ 3 = 24 |
4 | 72 ÷ 4 = 18 |
6 | 72 ÷ 6 = 12 |
8 | 72 ÷ 8 = 9 |
9 | 72 ÷ 9 = 8 |
12 | 72 ÷ 12 = 6 |
18 | 72 ÷ 18 = 4 |
24 | 72 ÷ 24 = 3 |
36 | 72 ÷ 36 = 2 |
Positive Numbers > 0
Since 72 ≥ 0 and it is an integer
72 is a positive number
Positive numbers including 0
with no decimal or fractions
Since 72 ≥ 0 and it is an integer
72 is a whole number
Since 72 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 + 4 + 6 + 8 + 9 + 12 + 18 + 24 + 36
Divisor Sum = 123
Since our divisor sum of 123 > 72
72 is an abundant number!
A number is even if it is divisible by 2
If not divisible by 2, it is odd
36 = | 72 |
2 |
Since 36 is an integer, 72 is divisible by 2
it is an even number
This can be written as A(72) = 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
72 to binary = 1001000
There are 2 1's, 72 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 12 items, we cannot form a pyramid
72 is not triangular
Is there an integer m such that n = m(m + 1)
The integer m = 8 satisifes our rectangular number property.
8(8 + 1) = 72
Does n2 ends with n
722 = 72 x 72 = 5184
Since 5184 does not end with 72
it is not automorphic (curious)
Do the digits of n alternate in the form abab
Since 72 < 100
We only perform the test on numbers > 99
Is there a number m such that m2 = n?
82 = 64 and 92 = 81 which do not equal 72
Therefore, 72 is not a square
Is there a number m such that m3 = n
43 = 64 and 53 = 125 ≠ 72
Therefore, 72 is not a cube
Is the number read backwards equal to the number?
The number read backwards is 27
Since 72 <> 27
it is not a palindrome
Is it both prime and a palindrome
From above, since 72 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 72 ≠ 1
then it is NOT repunit
Does 2n contain the consecutive digits 666?
272 = 4.7223664828696E+21
Since 272 does not have 666
72 is NOT an apocalyptic power
It satisfies the form:
n(3n - 1) | |
2 |
8(3(8 - 1) | |
2 |
8(24 - 1) | |
2 |
8(23) | |
2 |
184 | |
2 |
92 ← Since this does not equal 72
this is NOT a pentagonal number
7(3(7 - 1) | |
2 |
7(21 - 1) | |
2 |
7(20) | |
2 |
140 | |
2 |
70 ← Since this does not equal 72
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) = 72
Therefore 72 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 = 72
Therefore 72 is not heptagonal
Is there an integer m such that n = m(3m - 3)
No integer m exists such that m(3m - 2) = 72
Therefore 72 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 = 72
Therefore 72 is not nonagonal
Tetrahederal numbers satisfy the form:
n(n + 1)(n + 2) | |
6 |
7(7 + 1)(7 + 2) | |
6 |
7(8)(9) | |
6 |
504 | |
6 |
84 ← Since this does not equal 72
This is NOT a tetrahedral (Pyramidal) number
6(6 + 1)(6 + 2) | |
6 |
6(7)(8) | |
6 |
336 | |
6 |
56 ← Since this does not equal 72
This is NOT a tetrahedral (Pyramidal) number
Is equal to the square sum of it's m-th powers of its digits
72 is a 2 digit number, so m = 2
Square sum of digitsm = 72 + 22
Square sum of digitsm = 49 + 4
Square sum of digitsm = 53
Since 53 <> 72
72 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 72
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 72
This is NOT a Catalan number