What are the divisors of 5912?

1, 2, 4, 8, 739, 1478, 2956, 5912

There is a total of 8 positive divisors.
The sum of these divisors is 11100.
The arithmetic mean is 1387.5.

6 even divisors

2, 4, 8, 1478, 2956, 5912

2 odd divisors

1, 739

How to compute the divisors of 5912?

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 5912 by each of the numbers from 1 to 5912 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)

5912 / 1 = 5912 (the remainder is 0, so 1 is a divisor of 5912)
5912 / 2 = 2956 (the remainder is 0, so 2 is a divisor of 5912)
5912 / 3 = 1970.6666666667 (the remainder is 2, so 3 is not a divisor of 5912)
...
5912 / 5911 = 1.0001691761123 (the remainder is 1, so 5911 is not a divisor of 5912)
5912 / 5912 = 1 (the remainder is 0, so 5912 is a divisor of 5912)

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 5912 (i.e. 76.889531146964). 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 $\frac{N}{d} = D$ )

5912 / 1 = 5912 (the remainder is 0, so 1 and 5912 are divisors of 5912)
5912 / 2 = 2956 (the remainder is 0, so 2 and 2956 are divisors of 5912)
5912 / 3 = 1970.6666666667 (the remainder is 2, so 3 is not a divisor of 5912)
...
5912 / 75 = 78.826666666667 (the remainder is 62, so 75 is not a divisor of 5912)
5912 / 76 = 77.789473684211 (the remainder is 60, so 76 is not a divisor of 5912)