← Back to the labEVERY NUMBER HAS A STORY
01 / THE LAB
Number Explorer. — 0
One number. Many discoveries.
A CLOSER LOOK AT
0
- Prime or composite?
- Neither Prime numbers start at 2.
- Parity
- even Divisible by 2.
- Digit sum
- 0 0
- Fibonacci number?
- Yes F0 in the sequence (F0 = 0).
- Positive divisors
- Infinitely many Every positive integer divides zero.
- Perfect square?
- Yes 0 × 0 = 0
Prime factorization
Not defined for zero
Zero has no finite prime factorization.
- Binary BASE 2
- 0
- Hexadecimal BASE 16
- 0
03 / THE COLLECTIONOrdinary numbers.
Ordinary numbers.
Extraordinary stories.
Some numbers deserve
a second look.
The taxicab number
1,72901
An ordinary taxi. An extraordinary number.
The smallest number that is a sum of two positive cubes in two different ways.
A Fibonacci number
8902
A little rule with a long reach.
Add the previous two numbers. Repeat. Eventually, you meet 89.
A perfect number
2803
The beauty of adding up to yourself.
Its smaller positive divisors return exactly what you started with.
Kaprekar’s constant
6,17404
All these roads lead to 6174.
Rearrange four digits, subtract, and discover a surprisingly reliable destination.
A Fermat prime
65,53705
One step beyond a power of two.
Take two to the sixteenth power, add one, and find a prime.
An Armstrong number
15306
A number made from its own digits.
Cube each of its three digits. Their sum reconstructs the original number.
The multiplicative identity
107
Small enough to change nothing.
Multiply any number by one. It stays exactly itself.
The only even prime
208
The exception that proves itself.
Every other positive even number has an extra divisor. Two stands alone.