What are the divisors of 5876?

1, 2, 4, 13, 26, 52, 113, 226, 452, 1469, 2938, 5876

There is a total of 12 positive divisors.
The sum of these divisors is 11172.
The arithmetic mean is 931.

8 even divisors

2, 4, 26, 52, 226, 452, 2938, 5876

4 odd divisors

1, 13, 113, 1469

How to compute the divisors of 5876?

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 5876 by each of the numbers from 1 to 5876 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)

5876 / 1 = 5876 (the remainder is 0, so 1 is a divisor of 5876)
5876 / 2 = 2938 (the remainder is 0, so 2 is a divisor of 5876)
5876 / 3 = 1958.6666666667 (the remainder is 2, so 3 is not a divisor of 5876)
...
5876 / 5875 = 1.000170212766 (the remainder is 1, so 5875 is not a divisor of 5876)
5876 / 5876 = 1 (the remainder is 0, so 5876 is a divisor of 5876)

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 5876 (i.e. 76.655071586947). 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 $\frac{N}{d} = D$ )

5876 / 1 = 5876 (the remainder is 0, so 1 and 5876 are divisors of 5876)
5876 / 2 = 2938 (the remainder is 0, so 2 and 2938 are divisors of 5876)
5876 / 3 = 1958.6666666667 (the remainder is 2, so 3 is not a divisor of 5876)
...
5876 / 75 = 78.346666666667 (the remainder is 26, so 75 is not a divisor of 5876)
5876 / 76 = 77.315789473684 (the remainder is 24, so 76 is not a divisor of 5876)