What are the divisors of 5966?

1, 2, 19, 38, 157, 314, 2983, 5966

There is a total of 8 positive divisors.
The sum of these divisors is 9480.
The arithmetic mean is 1185.

4 even divisors

2, 38, 314, 5966

4 odd divisors

1, 19, 157, 2983

How to compute the divisors of 5966?

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 5966 by each of the numbers from 1 to 5966 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)

5966 / 1 = 5966 (the remainder is 0, so 1 is a divisor of 5966)
5966 / 2 = 2983 (the remainder is 0, so 2 is a divisor of 5966)
5966 / 3 = 1988.6666666667 (the remainder is 2, so 3 is not a divisor of 5966)
...
5966 / 5965 = 1.0001676445935 (the remainder is 1, so 5965 is not a divisor of 5966)
5966 / 5966 = 1 (the remainder is 0, so 5966 is a divisor of 5966)

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 5966 (i.e. 77.23988606931). 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 $\frac{N}{d} = D$ )

5966 / 1 = 5966 (the remainder is 0, so 1 and 5966 are divisors of 5966)
5966 / 2 = 2983 (the remainder is 0, so 2 and 2983 are divisors of 5966)
5966 / 3 = 1988.6666666667 (the remainder is 2, so 3 is not a divisor of 5966)
...
5966 / 76 = 78.5 (the remainder is 38, so 76 is not a divisor of 5966)
5966 / 77 = 77.480519480519 (the remainder is 37, so 77 is not a divisor of 5966)