What are the divisors of 2878?

1, 2, 1439, 2878

There is a total of 4 positive divisors.
The sum of these divisors is 4320.
The arithmetic mean is 1080.

2 even divisors

2, 2878

2 odd divisors

1, 1439

How to compute the divisors of 2878?

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 2878 by each of the numbers from 1 to 2878 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)

2878 / 1 = 2878 (the remainder is 0, so 1 is a divisor of 2878)
2878 / 2 = 1439 (the remainder is 0, so 2 is a divisor of 2878)
2878 / 3 = 959.33333333333 (the remainder is 1, so 3 is not a divisor of 2878)
...
2878 / 2877 = 1.0003475842892 (the remainder is 1, so 2877 is not a divisor of 2878)
2878 / 2878 = 1 (the remainder is 0, so 2878 is a divisor of 2878)

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 2878 (i.e. 53.646994324007). 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 $\frac{N}{d} = D$ )

2878 / 1 = 2878 (the remainder is 0, so 1 and 2878 are divisors of 2878)
2878 / 2 = 1439 (the remainder is 0, so 2 and 1439 are divisors of 2878)
2878 / 3 = 959.33333333333 (the remainder is 1, so 3 is not a divisor of 2878)
...
2878 / 52 = 55.346153846154 (the remainder is 18, so 52 is not a divisor of 2878)
2878 / 53 = 54.301886792453 (the remainder is 16, so 53 is not a divisor of 2878)