153 (number)
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| 153 | |
|---|---|
| Ordinal | 153 |
| Cardinal | 153rd |
| Factorization | <math>153 = 3^2 \cdot 17</math> |
| 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:
| <math>8^3 + 4^3</math> | = | 512 + 64 | = | 576 |
| <math>5^3 + 7^3 + 6^3</math> | = | 125 + 343 + 216 | = | 684 |
| <math>6^3 + 8^3 + 4^3</math> | = | 216 + 512 + 64 | = | 792 |
| <math>7^3 + 9^3 + 2^3</math> | = | 343 + 729 + 8 | = | 1080 |
| <math>1^3 + 0^3 + 8^3 + 0^3</math> | = | 1 + 0 + 512 + 0 | = | 513 |
| <math>5^3 + 1^3 + 3^3</math> | = | 125 + 1 + 27 | = | 153 |
| <math>1^3 + 5^3 + 3^3</math> | = | 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 <math>153 = 1^3 + 5^3 + 3^3</math>, it is a 3-narcissistic number, and it is a Friedman number since 153 = 3 * 51. It is a Harshad number in base 10.
One hundred (and) fifty-three is also
- 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.
[edit] See also
For the year, see AD 153.de:Hundertdreiundfünfzig es:Ciento cincuenta y tres fr:153 (nombre) ko:153 it:Centocinquantatré nl:153 (getal) ja:153 sl:153 (število) sv:153 (tal) vi:153 (số) zh:153
