What are the divisors of 5927?

1, 5927

There is a total of 2 positive divisors.
The sum of these divisors is 5928.
The arithmetic mean is 2964.

2 odd divisors

1, 5927

How to compute the divisors of 5927?

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 5927 by each of the numbers from 1 to 5927 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)

5927 / 1 = 5927 (the remainder is 0, so 1 is a divisor of 5927)
5927 / 2 = 2963.5 (the remainder is 1, so 2 is not a divisor of 5927)
5927 / 3 = 1975.6666666667 (the remainder is 2, so 3 is not a divisor of 5927)
...
5927 / 5926 = 1.0001687478907 (the remainder is 1, so 5926 is not a divisor of 5927)
5927 / 5927 = 1 (the remainder is 0, so 5927 is a divisor of 5927)

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 5927 (i.e. 76.987011891617). 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 $\frac{N}{d} = D$ )

5927 / 1 = 5927 (the remainder is 0, so 1 and 5927 are divisors of 5927)
5927 / 2 = 2963.5 (the remainder is 1, so 2 is not a divisor of 5927)
5927 / 3 = 1975.6666666667 (the remainder is 2, so 3 is not a divisor of 5927)
...
5927 / 75 = 79.026666666667 (the remainder is 2, so 75 is not a divisor of 5927)
5927 / 76 = 77.986842105263 (the remainder is 75, so 76 is not a divisor of 5927)