What are the divisors of 2864?

1, 2, 4, 8, 16, 179, 358, 716, 1432, 2864

There is a total of 10 positive divisors.
The sum of these divisors is 5580.
The arithmetic mean is 558.

8 even divisors

2, 4, 8, 16, 358, 716, 1432, 2864

2 odd divisors

1, 179

How to compute the divisors of 2864?

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 2864 by each of the numbers from 1 to 2864 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)

2864 / 1 = 2864 (the remainder is 0, so 1 is a divisor of 2864)
2864 / 2 = 1432 (the remainder is 0, so 2 is a divisor of 2864)
2864 / 3 = 954.66666666667 (the remainder is 2, so 3 is not a divisor of 2864)
...
2864 / 2863 = 1.0003492839679 (the remainder is 1, so 2863 is not a divisor of 2864)
2864 / 2864 = 1 (the remainder is 0, so 2864 is a divisor of 2864)

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 2864 (i.e. 53.516352641039). 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 $\frac{N}{d} = D$ )

2864 / 1 = 2864 (the remainder is 0, so 1 and 2864 are divisors of 2864)
2864 / 2 = 1432 (the remainder is 0, so 2 and 1432 are divisors of 2864)
2864 / 3 = 954.66666666667 (the remainder is 2, so 3 is not a divisor of 2864)
...
2864 / 52 = 55.076923076923 (the remainder is 4, so 52 is not a divisor of 2864)
2864 / 53 = 54.037735849057 (the remainder is 2, so 53 is not a divisor of 2864)