What are the divisors of 1?

There is a total of 1 positive divisors.
The sum of these divisors is 1.
The arithmetic mean is 1.

1 odd divisors

How to compute the divisors of 1?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 1 by each of the numbers from 1 to 1 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

1 / 1 = 1 (the remainder is 0, so 1 is a divisor of 1)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 1 (i.e. 1). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

1 / 1 = 1 (the remainder is 0, so 1 and 1 are divisors of 1)