Every number from 1 to 200
Prime factors, divisors, bases and Roman numerals — all worked out from the number itself. Nothing here was copied from a table.
The grid
Ten per row, twenty rows. The filled cells are primes — you can see the multiples of 2 and 5 drop out in columns.
Powers of two
This is why a byte stops at 256 and a port number stops at 65535.
Prime46
Nothing divides it but 1 and itself.
Square19
A number times itself — the dots lay out as a square.
Cube8
A number times itself three times — the dots stack into a cube.
Triangular19
The running total of 1, 2, 3 … — the dots stack into a triangle.
Fibonacci11
It sits in the run where each number is the sum of the two before it.
Power of two17
Two multiplied by itself. Every extra bit doubles it.
Perfect2
Add up its divisors except itself and you get the number back.
How to read this
- The prime factors are what the number is made of. The count and sum of divisors both follow from them.
- Add the divisors, take the number away, and you get perfect, abundant or deficient.
- The length of the binary form is the bit count. 255 taking eight digits is what a byte is.
- Collatz: halve it if even, triple it and add one if odd. The count is how many moves reach 1.
Frequently asked questions
Q. How many primes are there?
46 primes at or below 200. They are the filled cells in the grid.
Q. What is a perfect number?
One whose divisors, itself excluded, add back up to it. Below 200 there are only two: 6 and 28.
Q. Why list powers of two separately?
Because people looking up 255, 1024 or 65535 usually want where a byte or a port number ends, not number theory.
Q. How far do Roman numerals go?
To 3999. Above that there is no single agreed notation, so none is shown.
Q. Where does the data come from?
There is no data. Every value on these pages is computed from the number.