What are the divisors of 5922?

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 47, 63, 94, 126, 141, 282, 329, 423, 658, 846, 987, 1974, 2961, 5922

There is a total of 24 positive divisors.
The sum of these divisors is 14976.
The arithmetic mean is 624.

12 even divisors

2, 6, 14, 18, 42, 94, 126, 282, 658, 846, 1974, 5922

12 odd divisors

1, 3, 7, 9, 21, 47, 63, 141, 329, 423, 987, 2961

How to compute the divisors of 5922?

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 5922 by each of the numbers from 1 to 5922 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)

5922 / 1 = 5922 (the remainder is 0, so 1 is a divisor of 5922)
5922 / 2 = 2961 (the remainder is 0, so 2 is a divisor of 5922)
5922 / 3 = 1974 (the remainder is 0, so 3 is a divisor of 5922)
...
5922 / 5921 = 1.0001688903901 (the remainder is 1, so 5921 is not a divisor of 5922)
5922 / 5922 = 1 (the remainder is 0, so 5922 is a divisor of 5922)

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 5922 (i.e. 76.954532030284). 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 $\frac{N}{d} = D$ )

5922 / 1 = 5922 (the remainder is 0, so 1 and 5922 are divisors of 5922)
5922 / 2 = 2961 (the remainder is 0, so 2 and 2961 are divisors of 5922)
5922 / 3 = 1974 (the remainder is 0, so 3 and 1974 are divisors of 5922)
...
5922 / 75 = 78.96 (the remainder is 72, so 75 is not a divisor of 5922)
5922 / 76 = 77.921052631579 (the remainder is 70, so 76 is not a divisor of 5922)