What are the divisors of 5944?

1, 2, 4, 8, 743, 1486, 2972, 5944

There is a total of 8 positive divisors.
The sum of these divisors is 11160.
The arithmetic mean is 1395.

6 even divisors

2, 4, 8, 1486, 2972, 5944

2 odd divisors

1, 743

How to compute the divisors of 5944?

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 5944 by each of the numbers from 1 to 5944 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)

5944 / 1 = 5944 (the remainder is 0, so 1 is a divisor of 5944)
5944 / 2 = 2972 (the remainder is 0, so 2 is a divisor of 5944)
5944 / 3 = 1981.3333333333 (the remainder is 1, so 3 is not a divisor of 5944)
...
5944 / 5943 = 1.0001682651859 (the remainder is 1, so 5943 is not a divisor of 5944)
5944 / 5944 = 1 (the remainder is 0, so 5944 is a divisor of 5944)

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 5944 (i.e. 77.097341069586). 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 $\frac{N}{d} = D$ )

5944 / 1 = 5944 (the remainder is 0, so 1 and 5944 are divisors of 5944)
5944 / 2 = 2972 (the remainder is 0, so 2 and 2972 are divisors of 5944)
5944 / 3 = 1981.3333333333 (the remainder is 1, so 3 is not a divisor of 5944)
...
5944 / 76 = 78.210526315789 (the remainder is 16, so 76 is not a divisor of 5944)
5944 / 77 = 77.194805194805 (the remainder is 15, so 77 is not a divisor of 5944)