What are the divisors of 5870?

1, 2, 5, 10, 587, 1174, 2935, 5870

There is a total of 8 positive divisors.
The sum of these divisors is 10584.
The arithmetic mean is 1323.

4 even divisors

2, 10, 1174, 5870

4 odd divisors

1, 5, 587, 2935

How to compute the divisors of 5870?

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 5870 by each of the numbers from 1 to 5870 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)

5870 / 1 = 5870 (the remainder is 0, so 1 is a divisor of 5870)
5870 / 2 = 2935 (the remainder is 0, so 2 is a divisor of 5870)
5870 / 3 = 1956.6666666667 (the remainder is 2, so 3 is not a divisor of 5870)
...
5870 / 5869 = 1.000170386778 (the remainder is 1, so 5869 is not a divisor of 5870)
5870 / 5870 = 1 (the remainder is 0, so 5870 is a divisor of 5870)

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 5870 (i.e. 76.615925237512). 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 $\frac{N}{d} = D$ )

5870 / 1 = 5870 (the remainder is 0, so 1 and 5870 are divisors of 5870)
5870 / 2 = 2935 (the remainder is 0, so 2 and 2935 are divisors of 5870)
5870 / 3 = 1956.6666666667 (the remainder is 2, so 3 is not a divisor of 5870)
...
5870 / 75 = 78.266666666667 (the remainder is 20, so 75 is not a divisor of 5870)
5870 / 76 = 77.236842105263 (the remainder is 18, so 76 is not a divisor of 5870)