What are the divisors of 5890?

1, 2, 5, 10, 19, 31, 38, 62, 95, 155, 190, 310, 589, 1178, 2945, 5890

There is a total of 16 positive divisors.
The sum of these divisors is 11520.
The arithmetic mean is 720.

8 even divisors

2, 10, 38, 62, 190, 310, 1178, 5890

8 odd divisors

1, 5, 19, 31, 95, 155, 589, 2945

How to compute the divisors of 5890?

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 5890 by each of the numbers from 1 to 5890 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)

5890 / 1 = 5890 (the remainder is 0, so 1 is a divisor of 5890)
5890 / 2 = 2945 (the remainder is 0, so 2 is a divisor of 5890)
5890 / 3 = 1963.3333333333 (the remainder is 1, so 3 is not a divisor of 5890)
...
5890 / 5889 = 1.0001698081168 (the remainder is 1, so 5889 is not a divisor of 5890)
5890 / 5890 = 1 (the remainder is 0, so 5890 is a divisor of 5890)

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 5890 (i.e. 76.7463354174). 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 $\frac{N}{d} = D$ )

5890 / 1 = 5890 (the remainder is 0, so 1 and 5890 are divisors of 5890)
5890 / 2 = 2945 (the remainder is 0, so 2 and 2945 are divisors of 5890)
5890 / 3 = 1963.3333333333 (the remainder is 1, so 3 is not a divisor of 5890)
...
5890 / 75 = 78.533333333333 (the remainder is 40, so 75 is not a divisor of 5890)
5890 / 76 = 77.5 (the remainder is 38, so 76 is not a divisor of 5890)