What are the divisors of 5961?

1, 3, 1987, 5961

There is a total of 4 positive divisors.
The sum of these divisors is 7952.
The arithmetic mean is 1988.

4 odd divisors

1, 3, 1987, 5961

How to compute the divisors of 5961?

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 5961 by each of the numbers from 1 to 5961 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)

5961 / 1 = 5961 (the remainder is 0, so 1 is a divisor of 5961)
5961 / 2 = 2980.5 (the remainder is 1, so 2 is not a divisor of 5961)
5961 / 3 = 1987 (the remainder is 0, so 3 is a divisor of 5961)
...
5961 / 5960 = 1.0001677852349 (the remainder is 1, so 5960 is not a divisor of 5961)
5961 / 5961 = 1 (the remainder is 0, so 5961 is a divisor of 5961)

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 5961 (i.e. 77.20751258783). 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 $\frac{N}{d} = D$ )

5961 / 1 = 5961 (the remainder is 0, so 1 and 5961 are divisors of 5961)
5961 / 2 = 2980.5 (the remainder is 1, so 2 is not a divisor of 5961)
5961 / 3 = 1987 (the remainder is 0, so 3 and 1987 are divisors of 5961)
...
5961 / 76 = 78.434210526316 (the remainder is 33, so 76 is not a divisor of 5961)
5961 / 77 = 77.415584415584 (the remainder is 32, so 77 is not a divisor of 5961)