What are the divisors of 5955?

1, 3, 5, 15, 397, 1191, 1985, 5955

There is a total of 8 positive divisors.
The sum of these divisors is 9552.
The arithmetic mean is 1194.

8 odd divisors

1, 3, 5, 15, 397, 1191, 1985, 5955

How to compute the divisors of 5955?

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 5955 by each of the numbers from 1 to 5955 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)

5955 / 1 = 5955 (the remainder is 0, so 1 is a divisor of 5955)
5955 / 2 = 2977.5 (the remainder is 1, so 2 is not a divisor of 5955)
5955 / 3 = 1985 (the remainder is 0, so 3 is a divisor of 5955)
...
5955 / 5954 = 1.0001679543164 (the remainder is 1, so 5954 is not a divisor of 5955)
5955 / 5955 = 1 (the remainder is 0, so 5955 is a divisor of 5955)

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 5955 (i.e. 77.168646482882). 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 $\frac{N}{d} = D$ )

5955 / 1 = 5955 (the remainder is 0, so 1 and 5955 are divisors of 5955)
5955 / 2 = 2977.5 (the remainder is 1, so 2 is not a divisor of 5955)
5955 / 3 = 1985 (the remainder is 0, so 3 and 1985 are divisors of 5955)
...
5955 / 76 = 78.355263157895 (the remainder is 27, so 76 is not a divisor of 5955)
5955 / 77 = 77.337662337662 (the remainder is 26, so 77 is not a divisor of 5955)