What are the divisors of 5860?

1, 2, 4, 5, 10, 20, 293, 586, 1172, 1465, 2930, 5860

There is a total of 12 positive divisors.
The sum of these divisors is 12348.
The arithmetic mean is 1029.

8 even divisors

2, 4, 10, 20, 586, 1172, 2930, 5860

4 odd divisors

1, 5, 293, 1465

How to compute the divisors of 5860?

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 5860 by each of the numbers from 1 to 5860 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)

5860 / 1 = 5860 (the remainder is 0, so 1 is a divisor of 5860)
5860 / 2 = 2930 (the remainder is 0, so 2 is a divisor of 5860)
5860 / 3 = 1953.3333333333 (the remainder is 1, so 3 is not a divisor of 5860)
...
5860 / 5859 = 1.00017067759 (the remainder is 1, so 5859 is not a divisor of 5860)
5860 / 5860 = 1 (the remainder is 0, so 5860 is a divisor of 5860)

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 5860 (i.e. 76.550636836019). 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 $\frac{N}{d} = D$ )

5860 / 1 = 5860 (the remainder is 0, so 1 and 5860 are divisors of 5860)
5860 / 2 = 2930 (the remainder is 0, so 2 and 2930 are divisors of 5860)
5860 / 3 = 1953.3333333333 (the remainder is 1, so 3 is not a divisor of 5860)
...
5860 / 75 = 78.133333333333 (the remainder is 10, so 75 is not a divisor of 5860)
5860 / 76 = 77.105263157895 (the remainder is 8, so 76 is not a divisor of 5860)