What are the divisors of 2865?

1, 3, 5, 15, 191, 573, 955, 2865

There is a total of 8 positive divisors.
The sum of these divisors is 4608.
The arithmetic mean is 576.

8 odd divisors

1, 3, 5, 15, 191, 573, 955, 2865

How to compute the divisors of 2865?

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 2865 by each of the numbers from 1 to 2865 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)

2865 / 1 = 2865 (the remainder is 0, so 1 is a divisor of 2865)
2865 / 2 = 1432.5 (the remainder is 1, so 2 is not a divisor of 2865)
2865 / 3 = 955 (the remainder is 0, so 3 is a divisor of 2865)
...
2865 / 2864 = 1.0003491620112 (the remainder is 1, so 2864 is not a divisor of 2865)
2865 / 2865 = 1 (the remainder is 0, so 2865 is a divisor of 2865)

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 2865 (i.e. 53.525694764291). 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 $\frac{N}{d} = D$ )

2865 / 1 = 2865 (the remainder is 0, so 1 and 2865 are divisors of 2865)
2865 / 2 = 1432.5 (the remainder is 1, so 2 is not a divisor of 2865)
2865 / 3 = 955 (the remainder is 0, so 3 and 955 are divisors of 2865)
...
2865 / 52 = 55.096153846154 (the remainder is 5, so 52 is not a divisor of 2865)
2865 / 53 = 54.056603773585 (the remainder is 3, so 53 is not a divisor of 2865)