Mathematics is something beautiful if you can see how interesting each natural number is. All numbers are interesting, but some numbers are more interesting than others.
In my earlier posts I have discussed about such interesting numbers –
Palindromes , Munchausen Number, beauty of numbers, Ramanujan Number
One such very interesting number is 153. I figured out few properties of 153 myself and felt proud on my observations. However when I researched more I was embarrassed at the paucity of my observations. I swear now that each number is a study in itself.
I am listing below some attention-grabbing and curious property of 153. For better understanding, I have linked certain terms to wikipedia-
Properties of 153
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 a pluperfect digital invariant (PPDI), an Armstrong number or a plus perfect number) is a number that is the sum of its own digits each raised to the power of the number of digits. Source: wikipedia
153 can be expressed as the sum of all integers from 1 to 17.
153 = 1+2+3+4+………..+16+17
Hence it can also be called a triangular number. Reverse of 153, i.e. 351 is also a triangular number, 153 can be termed as a reversible triangular number.
153 is equal to the sum of factorials of number from 1 to 5 –
153 = 1! + 2! + 3! + 4! + 5!
Sum of the digits of 153 is a perfect square-
1 + 5 + 3 = 9 = 3^2
Sum of all the divisors of 153 (except itself) is also a perfect square-
1 + 3 + 9 + 17 + 51 = 81 = 9^2
153 can be expressed as the product of two numbers formed from its own digits-
153 = 3 x 51
Square root of 153 = 12.369 is the amount of full moons in one year. Isn’t that interesting?
Other Observations on 153 –
1^0 + 5^1 + 3^2 = 15
1^1 + 5^2 + 3^3 = 53
153 if added to its reverse351,we get 504.
153 + 351 = 504
Square of 504 is the smallest square which can be expressed as the product of two different non-square numbers which are reverse of one another:
504^2 = 288 x 882
I hope now you find the number 153 as interesting as I did. I have purposefully not mentioned few other interesting properties of 153. Now the ball is in your court. Share more such properties with other readers by posting a comment below.
Suggested by Mohit Singhvi
Written by Vineet Patawari