What are the divisors of 5871?

1, 3, 19, 57, 103, 309, 1957, 5871

There is a total of 8 positive divisors.
The sum of these divisors is 8320.
The arithmetic mean is 1040.

8 odd divisors

1, 3, 19, 57, 103, 309, 1957, 5871

How to compute the divisors of 5871?

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 5871 by each of the numbers from 1 to 5871 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)

5871 / 1 = 5871 (the remainder is 0, so 1 is a divisor of 5871)
5871 / 2 = 2935.5 (the remainder is 1, so 2 is not a divisor of 5871)
5871 / 3 = 1957 (the remainder is 0, so 3 is a divisor of 5871)
...
5871 / 5870 = 1.0001703577513 (the remainder is 1, so 5870 is not a divisor of 5871)
5871 / 5871 = 1 (the remainder is 0, so 5871 is a divisor of 5871)

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 5871 (i.e. 76.622451017962). 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 $\frac{N}{d} = D$ )

5871 / 1 = 5871 (the remainder is 0, so 1 and 5871 are divisors of 5871)
5871 / 2 = 2935.5 (the remainder is 1, so 2 is not a divisor of 5871)
5871 / 3 = 1957 (the remainder is 0, so 3 and 1957 are divisors of 5871)
...
5871 / 75 = 78.28 (the remainder is 21, so 75 is not a divisor of 5871)
5871 / 76 = 77.25 (the remainder is 19, so 76 is not a divisor of 5871)