What are the divisors of 5878?

1, 2, 2939, 5878

There is a total of 4 positive divisors.
The sum of these divisors is 8820.
The arithmetic mean is 2205.

2 even divisors

2, 5878

2 odd divisors

1, 2939

How to compute the divisors of 5878?

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 5878 by each of the numbers from 1 to 5878 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)

5878 / 1 = 5878 (the remainder is 0, so 1 is a divisor of 5878)
5878 / 2 = 2939 (the remainder is 0, so 2 is a divisor of 5878)
5878 / 3 = 1959.3333333333 (the remainder is 1, so 3 is not a divisor of 5878)
...
5878 / 5877 = 1.0001701548409 (the remainder is 1, so 5877 is not a divisor of 5878)
5878 / 5878 = 1 (the remainder is 0, so 5878 is a divisor of 5878)

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 5878 (i.e. 76.668115928331). 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 $\frac{N}{d} = D$ )

5878 / 1 = 5878 (the remainder is 0, so 1 and 5878 are divisors of 5878)
5878 / 2 = 2939 (the remainder is 0, so 2 and 2939 are divisors of 5878)
5878 / 3 = 1959.3333333333 (the remainder is 1, so 3 is not a divisor of 5878)
...
5878 / 75 = 78.373333333333 (the remainder is 28, so 75 is not a divisor of 5878)
5878 / 76 = 77.342105263158 (the remainder is 26, so 76 is not a divisor of 5878)