Mathematics is something beautiful if you
can see how interesting each natural number is. The moment we understand the
properties of numbers, mathematics become so simple and exciting.

One such very interesting number is 153.
Here are some attention-grabbing and curious properties of 153.

**Property 1**

153 is the smallest number which can be
expressed as the sum of cubes of its digits

153 = 1

^{3}+ 5^{3}+ 3^{3}
Because of this property 153 is called a

__narcissistic number__(also known as an Armstrong number or a plus perfect number) i.e. a number that is cubes of each digit of the number is equal to the number itself.**Property 2**

153 can be expressed as the sum of all
integers from 1 to 17.

153 = 1+2+3+4+………..+16+17

So, it can be called a triangular
number. In other words, 153 is the 17

^{th}triangular number.
Reverse of 153, i.e. 351 is also a
triangular number; hence, 153 can be termed as a reversible triangular number.

**Property 3**

153 is equal to the sum of factorials of
number from 1 to 5 –

153 = 1! + 2! + 3! + 4! + 5!

**Property 4**

The Sum of the digits of 153 is a perfect
square-

1 + 5 + 3 = 9 = 3

^{2}**1 + 3 + 9 + 17 + 51 = 81 = 9**

^{2}Aliquot divisors of a number are all the divisors of that number excluding the number itself but including 1. It is seen that the sum of aliquot divisors of 153 is the square of the sum of the digits of 153.

**Property 5**

153 can be expressed as the product of two
numbers formed by its own digits-

**153 = 3 x 51**

Note that the digits used in multipliers
are same as in product.

**Property 6**

**1**

^{0}+ 5^{1}+ 3^{2}= 15 = 1 * 5 * 3**Property 7**

On adding the number

**153**to its reverse,**504**is obtained, whose square is the smallest square which can be expressed as the product of two different non-square numbers which are reverse of one another:**153 + 351 = 504**

**504**

^{2}= 288 x 882**Property 8**

153 is divisible by the sum of its own
digits:

**153 / (1 + 5 + 3) = 17**

**Property 9**

(12345678
+ 87654321) *

**153**+**153**=**15300000000**.
The
zero is repeated 8 times.

**Property 10**

Square root of 153 (i.e. 12.369) is the
amount of full moons in one year.

Isn’t that interesting?

**Property 11**

Palindromic side-effects!

A
magic moment occurs when working out its reciprocal

1 ÷ 153 =
0,006535947712418300653594...

"Take
all the significant figures, multiply by

**17**, and__multiples of 17__, and watch the pattern formed:"
65359477124183
x

**17**=**1111111111111111**
65359477124183
x

**34**=**2222222222222222**
65359477124183
x

**51**=**3333333333333333**
65359477124183
x

**68**=**4444444444444444**
65359477124183
x

**85**=**5555555555555555**
65359477124183
x

**102**=**6666666666666666**
65359477124183
x

**119**=**7777777777777777**
65359477124183
x

**136**=**8888888888888888**
65359477124183
x

**153**=**9999999999999999**
However, this property is true for any
number, whose reciprocal is a repeating number.

**Property 12**

“What’s exceptionally cool, though, is that if you
take any three-digit multiple of 3, and then add the third power of its digits,
and then add the third power of the digits of the result, and keep doing that,
you’ll always get back to 153.”

Take 369 for instance which is a multiple of 3.

Sum of 3

^{rd}power of the digits of 369 = 3^{3}+ 6^{3}+ 9^{3}= 27 + 216 + 729 = 972
Now, sum of 3

^{rd}power of the digits of 972 = 9^{3}+ 7^{3}+ 2^{3}= 729 + 343 + 8 = 1080
Sum of 3

^{rd}power of the digits of 1080 = 1^{3}+ 0^{3}+ 8^{3}+ 0^{3}= 1 +0+ 512 + 0 = 513
Sum of 3

^{rd}power of the digits of 513 = 5^{3}+ 1^{3}+ 3^{3}= 125 + 1 + 27 =__153__
It's nice to know I'm not the only one that gets a kick out of curious properties of numbers. Lately, I played with the number 76923. When 76923 is multiplied by the consecutive numbers from 1 to 12 in a particular order it produces remarkable or ‘mystical’ outcomes, which can be represented in Latin Squares. Combining the two Latin Squares results in a Magic Square with a magic sum of 54. See how it’s done: http://www.glennwestmore.com.au/the-mystic-number-76923/

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