What are the divisors of 5891?

1, 43, 137, 5891

There is a total of 4 positive divisors.
The sum of these divisors is 6072.
The arithmetic mean is 1518.

4 odd divisors

1, 43, 137, 5891

How to compute the divisors of 5891?

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 5891 by each of the numbers from 1 to 5891 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)

5891 / 1 = 5891 (the remainder is 0, so 1 is a divisor of 5891)
5891 / 2 = 2945.5 (the remainder is 1, so 2 is not a divisor of 5891)
5891 / 3 = 1963.6666666667 (the remainder is 2, so 3 is not a divisor of 5891)
...
5891 / 5890 = 1.0001697792869 (the remainder is 1, so 5890 is not a divisor of 5891)
5891 / 5891 = 1 (the remainder is 0, so 5891 is a divisor of 5891)

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 5891 (i.e. 76.752850109947). 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 $\frac{N}{d} = D$ )

5891 / 1 = 5891 (the remainder is 0, so 1 and 5891 are divisors of 5891)
5891 / 2 = 2945.5 (the remainder is 1, so 2 is not a divisor of 5891)
5891 / 3 = 1963.6666666667 (the remainder is 2, so 3 is not a divisor of 5891)
...
5891 / 75 = 78.546666666667 (the remainder is 41, so 75 is not a divisor of 5891)
5891 / 76 = 77.513157894737 (the remainder is 39, so 76 is not a divisor of 5891)