153 (number)

From Wikipedia, the free encyclopedia

153
Ordinal	153
Cardinal	153rd
Factorization	$153 = 3^2 \cdot 17$
Divisors	1, 3, 9, 17, 51, 153
Roman numeral	CLIII
Binary	10011001
Octal	231
Hexadecimal	99

One hundred (and) fifty-three is the natural number following one hundred (and) fifty-two and preceding one hundred (and) fifty-four.

As a triangular number, it is the sum of the first 17 integers, and also the sum of the first five factorials. It is also a hexagonal number.

The distinct prime factors of 153 add up to 20, and so do the ones of 154, hence the two form a Ruth-Aaron pair.

Another interesting feature of the number 153 is that it's the limit of the following algorithm:

Take a random number, divisible by three.
Split that number into its base 10 digits.
Take the sum of their cubes.
Go to the second step.

An example, starting with the number 84:

$83 + 4 3$	=	512 + 64	=	576
$53 + 7 3 + 6 3$	=	125 + 343 + 216	=	684
$63 + 8 3 + 4 3$	=	216 + 512 + 64	=	792
$73 + 9 3 + 2 3$	=	343 + 729 + 8	=	1080
$13 + 0 3 + 8 3 + 0 3$	=	1 + 0 + 512 + 0	=	513
$53 + 1 3 + 3 3$	=	125 + 1 + 27	=	153
$13 + 5 3 + 3 3$	=	1 + 125 + 27	=	153

Evagrius Ponticus considered 153 to represent a harmonization of contrasts, since 153 = 100 + 28 + 25, with 100 representing a square, 28 a triangle and 25 a circle.

Since $153 = 1 3 + 5 3 + 3 3$ , it is a 3-narcissistic number, and it is a Friedman number since 153 = 3 * 51. It is a Harshad number in base 10.

[edit] Other usages

The number of fish caught in the Catch of 153 fish in the biblical narrative of the Gospel of John.
Considered by St. Augustine to represent seven gifts of the Holy Spirit and ten requirements of God.
The frequency of the longwave transmitters Donebach, Ingoy and Braşov in kilohertz.
The ordinal number of the coat of arms of Komi Republic in the State Heraldic Register of the Russian Federation.