What are the divisors of 5963?

1, 67, 89, 5963

There is a total of 4 positive divisors.
The sum of these divisors is 6120.
The arithmetic mean is 1530.

4 odd divisors

1, 67, 89, 5963

How to compute the divisors of 5963?

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 5963 by each of the numbers from 1 to 5963 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)

5963 / 1 = 5963 (the remainder is 0, so 1 is a divisor of 5963)
5963 / 2 = 2981.5 (the remainder is 1, so 2 is not a divisor of 5963)
5963 / 3 = 1987.6666666667 (the remainder is 2, so 3 is not a divisor of 5963)
...
5963 / 5962 = 1.00016772895 (the remainder is 1, so 5962 is not a divisor of 5963)
5963 / 5963 = 1 (the remainder is 0, so 5963 is a divisor of 5963)

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 5963 (i.e. 77.220463609072). 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 $\frac{N}{d} = D$ )

5963 / 1 = 5963 (the remainder is 0, so 1 and 5963 are divisors of 5963)
5963 / 2 = 2981.5 (the remainder is 1, so 2 is not a divisor of 5963)
5963 / 3 = 1987.6666666667 (the remainder is 2, so 3 is not a divisor of 5963)
...
5963 / 76 = 78.460526315789 (the remainder is 35, so 76 is not a divisor of 5963)
5963 / 77 = 77.441558441558 (the remainder is 34, so 77 is not a divisor of 5963)