What are the divisors of 4588?

1, 2, 4, 31, 37, 62, 74, 124, 148, 1147, 2294, 4588

There is a total of 12 positive divisors.
The sum of these divisors is 8512.
The arithmetic mean is 709.33333333333.

8 even divisors

2, 4, 62, 74, 124, 148, 2294, 4588

4 odd divisors

1, 31, 37, 1147

How to compute the divisors of 4588?

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 4588 by each of the numbers from 1 to 4588 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)

4588 / 1 = 4588 (the remainder is 0, so 1 is a divisor of 4588)
4588 / 2 = 2294 (the remainder is 0, so 2 is a divisor of 4588)
4588 / 3 = 1529.3333333333 (the remainder is 1, so 3 is not a divisor of 4588)
...
4588 / 4587 = 1.0002180074123 (the remainder is 1, so 4587 is not a divisor of 4588)
4588 / 4588 = 1 (the remainder is 0, so 4588 is a divisor of 4588)

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 4588 (i.e. 67.734776887504). 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 $\frac{N}{d} = D$ )

4588 / 1 = 4588 (the remainder is 0, so 1 and 4588 are divisors of 4588)
4588 / 2 = 2294 (the remainder is 0, so 2 and 2294 are divisors of 4588)
4588 / 3 = 1529.3333333333 (the remainder is 1, so 3 is not a divisor of 4588)
...
4588 / 66 = 69.515151515152 (the remainder is 34, so 66 is not a divisor of 4588)
4588 / 67 = 68.477611940299 (the remainder is 32, so 67 is not a divisor of 4588)