What are the divisors of 1588?

1, 2, 4, 397, 794, 1588

There is a total of 6 positive divisors.
The sum of these divisors is 2786.
The arithmetic mean is 464.33333333333.

4 even divisors

2, 4, 794, 1588

2 odd divisors

1, 397

How to compute the divisors of 1588?

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 1588 by each of the numbers from 1 to 1588 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)

1588 / 1 = 1588 (the remainder is 0, so 1 is a divisor of 1588)
1588 / 2 = 794 (the remainder is 0, so 2 is a divisor of 1588)
1588 / 3 = 529.33333333333 (the remainder is 1, so 3 is not a divisor of 1588)
...
1588 / 1587 = 1.0006301197227 (the remainder is 1, so 1587 is not a divisor of 1588)
1588 / 1588 = 1 (the remainder is 0, so 1588 is a divisor of 1588)

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 1588 (i.e. 39.849717690343). 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 $\frac{N}{d} = D$ )

1588 / 1 = 1588 (the remainder is 0, so 1 and 1588 are divisors of 1588)
1588 / 2 = 794 (the remainder is 0, so 2 and 794 are divisors of 1588)
1588 / 3 = 529.33333333333 (the remainder is 1, so 3 is not a divisor of 1588)
...
1588 / 38 = 41.789473684211 (the remainder is 30, so 38 is not a divisor of 1588)
1588 / 39 = 40.717948717949 (the remainder is 28, so 39 is not a divisor of 1588)