What are the divisors of 5892?

1, 2, 3, 4, 6, 12, 491, 982, 1473, 1964, 2946, 5892

There is a total of 12 positive divisors.
The sum of these divisors is 13776.
The arithmetic mean is 1148.

8 even divisors

2, 4, 6, 12, 982, 1964, 2946, 5892

4 odd divisors

1, 3, 491, 1473

How to compute the divisors of 5892?

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 5892 by each of the numbers from 1 to 5892 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)

5892 / 1 = 5892 (the remainder is 0, so 1 is a divisor of 5892)
5892 / 2 = 2946 (the remainder is 0, so 2 is a divisor of 5892)
5892 / 3 = 1964 (the remainder is 0, so 3 is a divisor of 5892)
...
5892 / 5891 = 1.0001697504668 (the remainder is 1, so 5891 is not a divisor of 5892)
5892 / 5892 = 1 (the remainder is 0, so 5892 is a divisor of 5892)

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 5892 (i.e. 76.759364249582). 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 $\frac{N}{d} = D$ )

5892 / 1 = 5892 (the remainder is 0, so 1 and 5892 are divisors of 5892)
5892 / 2 = 2946 (the remainder is 0, so 2 and 2946 are divisors of 5892)
5892 / 3 = 1964 (the remainder is 0, so 3 and 1964 are divisors of 5892)
...
5892 / 75 = 78.56 (the remainder is 42, so 75 is not a divisor of 5892)
5892 / 76 = 77.526315789474 (the remainder is 40, so 76 is not a divisor of 5892)