What are the divisors of 2859?

1, 3, 953, 2859

There is a total of 4 positive divisors.
The sum of these divisors is 3816.
The arithmetic mean is 954.

4 odd divisors

1, 3, 953, 2859

How to compute the divisors of 2859?

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 2859 by each of the numbers from 1 to 2859 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)

2859 / 1 = 2859 (the remainder is 0, so 1 is a divisor of 2859)
2859 / 2 = 1429.5 (the remainder is 1, so 2 is not a divisor of 2859)
2859 / 3 = 953 (the remainder is 0, so 3 is a divisor of 2859)
...
2859 / 2858 = 1.0003498950315 (the remainder is 1, so 2858 is not a divisor of 2859)
2859 / 2859 = 1 (the remainder is 0, so 2859 is a divisor of 2859)

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 2859 (i.e. 53.469617541179). 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 $\frac{N}{d} = D$ )

2859 / 1 = 2859 (the remainder is 0, so 1 and 2859 are divisors of 2859)
2859 / 2 = 1429.5 (the remainder is 1, so 2 is not a divisor of 2859)
2859 / 3 = 953 (the remainder is 0, so 3 and 953 are divisors of 2859)
...
2859 / 52 = 54.980769230769 (the remainder is 51, so 52 is not a divisor of 2859)
2859 / 53 = 53.943396226415 (the remainder is 50, so 53 is not a divisor of 2859)