The number 1 — factors and divisors
Deficient
1 is neither prime nor composite. Only itself divides it, so it has 1 divisor.
Its divisors, itself excluded, add up to less than the number.
Families it belongs to
A number times itself — the dots lay out as a square.
A number times itself three times — the dots stack into a cube.
The running total of 1, 2, 3 … — the dots stack into a triangle.
It sits in the run where each number is the sum of the two before it.
Two multiplied by itself. Every extra bit doubles it.
Laid out as dots
It fits as 1 × 1. The more divisors, the closer to a square.
- Prime factors
- Divisors
- 1
- Sum of divisors
- 1
- Sum without itself
- 0
- Coprime below it
- 1
- Digit sum
- 1
- Digital root
- 1
- Roman numeral
- I
- Binary
- 1
- Octal
- 1
- Hexadecimal
- 1
- Base 36
- 1
- Bits
- 1 bit
- Collatz steps
- 0 steps · peaks at 1
- Prime before
- None
- Prime after
- 2
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.
Numbers either side
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. Is 1 a prime number?
No. It breaks down into .
Q. What are the divisors of 1?
1 — 1 divisor in all, adding up to 1.
Q. How is 1 written in binary?
1, which is 1 bits. In hexadecimal it is 1.
Q. How many Collatz steps does 1 take?
It reaches 1 in 0, peaking at 1 on the way.