What are the divisors of 5932?

1, 2, 4, 1483, 2966, 5932

There is a total of 6 positive divisors.
The sum of these divisors is 10388.
The arithmetic mean is 1731.3333333333.

4 even divisors

2, 4, 2966, 5932

2 odd divisors

1, 1483

How to compute the divisors of 5932?

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 5932 by each of the numbers from 1 to 5932 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)

5932 / 1 = 5932 (the remainder is 0, so 1 is a divisor of 5932)
5932 / 2 = 2966 (the remainder is 0, so 2 is a divisor of 5932)
5932 / 3 = 1977.3333333333 (the remainder is 1, so 3 is not a divisor of 5932)
...
5932 / 5931 = 1.0001686056314 (the remainder is 1, so 5931 is not a divisor of 5932)
5932 / 5932 = 1 (the remainder is 0, so 5932 is a divisor of 5932)

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 5932 (i.e. 77.019478055879). 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 $\frac{N}{d} = D$ )

5932 / 1 = 5932 (the remainder is 0, so 1 and 5932 are divisors of 5932)
5932 / 2 = 2966 (the remainder is 0, so 2 and 2966 are divisors of 5932)
5932 / 3 = 1977.3333333333 (the remainder is 1, so 3 is not a divisor of 5932)
...
5932 / 76 = 78.052631578947 (the remainder is 4, so 76 is not a divisor of 5932)
5932 / 77 = 77.038961038961 (the remainder is 3, so 77 is not a divisor of 5932)