What are the divisors of 2858?

1, 2, 1429, 2858

There is a total of 4 positive divisors.
The sum of these divisors is 4290.
The arithmetic mean is 1072.5.

2 even divisors

2, 2858

2 odd divisors

1, 1429

How to compute the divisors of 2858?

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 2858 by each of the numbers from 1 to 2858 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)

2858 / 1 = 2858 (the remainder is 0, so 1 is a divisor of 2858)
2858 / 2 = 1429 (the remainder is 0, so 2 is a divisor of 2858)
2858 / 3 = 952.66666666667 (the remainder is 2, so 3 is not a divisor of 2858)
...
2858 / 2857 = 1.0003500175009 (the remainder is 1, so 2857 is not a divisor of 2858)
2858 / 2858 = 1 (the remainder is 0, so 2858 is a divisor of 2858)

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 2858 (i.e. 53.460265618495). 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 $\frac{N}{d} = D$ )

2858 / 1 = 2858 (the remainder is 0, so 1 and 2858 are divisors of 2858)
2858 / 2 = 1429 (the remainder is 0, so 2 and 1429 are divisors of 2858)
2858 / 3 = 952.66666666667 (the remainder is 2, so 3 is not a divisor of 2858)
...
2858 / 52 = 54.961538461538 (the remainder is 50, so 52 is not a divisor of 2858)
2858 / 53 = 53.924528301887 (the remainder is 49, so 53 is not a divisor of 2858)