What are the divisors of 5967?

1, 3, 9, 13, 17, 27, 39, 51, 117, 153, 221, 351, 459, 663, 1989, 5967

There is a total of 16 positive divisors.
The sum of these divisors is 10080.
The arithmetic mean is 630.

16 odd divisors

1, 3, 9, 13, 17, 27, 39, 51, 117, 153, 221, 351, 459, 663, 1989, 5967

How to compute the divisors of 5967?

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 5967 by each of the numbers from 1 to 5967 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)

5967 / 1 = 5967 (the remainder is 0, so 1 is a divisor of 5967)
5967 / 2 = 2983.5 (the remainder is 1, so 2 is not a divisor of 5967)
5967 / 3 = 1989 (the remainder is 0, so 3 is a divisor of 5967)
...
5967 / 5966 = 1.0001676164935 (the remainder is 1, so 5966 is not a divisor of 5967)
5967 / 5967 = 1 (the remainder is 0, so 5967 is a divisor of 5967)

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 5967 (i.e. 77.246359137502). 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 $\frac{N}{d} = D$ )

5967 / 1 = 5967 (the remainder is 0, so 1 and 5967 are divisors of 5967)
5967 / 2 = 2983.5 (the remainder is 1, so 2 is not a divisor of 5967)
5967 / 3 = 1989 (the remainder is 0, so 3 and 1989 are divisors of 5967)
...
5967 / 76 = 78.513157894737 (the remainder is 39, so 76 is not a divisor of 5967)
5967 / 77 = 77.493506493506 (the remainder is 38, so 77 is not a divisor of 5967)