What are the divisors of 5989?

1, 53, 113, 5989

There is a total of 4 positive divisors.
The sum of these divisors is 6156.
The arithmetic mean is 1539.

4 odd divisors

1, 53, 113, 5989

How to compute the divisors of 5989?

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 5989 by each of the numbers from 1 to 5989 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)

5989 / 1 = 5989 (the remainder is 0, so 1 is a divisor of 5989)
5989 / 2 = 2994.5 (the remainder is 1, so 2 is not a divisor of 5989)
5989 / 3 = 1996.3333333333 (the remainder is 1, so 3 is not a divisor of 5989)
...
5989 / 5988 = 1.000167000668 (the remainder is 1, so 5988 is not a divisor of 5989)
5989 / 5989 = 1 (the remainder is 0, so 5989 is a divisor of 5989)

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 5989 (i.e. 77.388629655783). 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 $\frac{N}{d} = D$ )

5989 / 1 = 5989 (the remainder is 0, so 1 and 5989 are divisors of 5989)
5989 / 2 = 2994.5 (the remainder is 1, so 2 is not a divisor of 5989)
5989 / 3 = 1996.3333333333 (the remainder is 1, so 3 is not a divisor of 5989)
...
5989 / 76 = 78.802631578947 (the remainder is 61, so 76 is not a divisor of 5989)
5989 / 77 = 77.779220779221 (the remainder is 60, so 77 is not a divisor of 5989)