Interesting Properties of 153

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 – 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

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 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

Property 2

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.

Property 3

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

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

Property 4

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

Property 5

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

153 = 3 x 51

Property 6

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 Vineet Patawari

Hi, I'm Vineet Patawari. I fell in love with numbers after being scared of them for quite some time. Now, I'm here to make you feel comfortable with numbers and help you get rid of Math Phobia!

11 thoughts to “Interesting Properties of 153”

1. Josef Grießhaber says:

I know three other secrets abut 153

2. VIJAY BHASKAR says:

REALLY ITS AMAZING

3. pradeep says:

Really keen observation

4. chai says:

dats really interesting.gud 1 friend

5. vivek says:

gr8 observation

6. sameer aryan says:

hiii truly d mind blowing properties of 153
i wish to see mnore abt each numbrs

7. jignesh says:

8. Arun Dev says:

hey it z very interstiong, all d property are coorect.
wow beautiful 153

9. aqua says:

really int
ialways search 4 a no to print in my t shirt…which is unique…now i got it with gud resion…

10. Aruna says:

where can I check the answers for these to make sure my kids did it correct