What are the divisors of 1594?

1, 2, 797, 1594

There is a total of 4 positive divisors.
The sum of these divisors is 2394.
The arithmetic mean is 598.5.

2 even divisors

2, 1594

2 odd divisors

1, 797

How to compute the divisors of 1594?

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 1594 by each of the numbers from 1 to 1594 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)

1594 / 1 = 1594 (the remainder is 0, so 1 is a divisor of 1594)
1594 / 2 = 797 (the remainder is 0, so 2 is a divisor of 1594)
1594 / 3 = 531.33333333333 (the remainder is 1, so 3 is not a divisor of 1594)
...
1594 / 1593 = 1.0006277463905 (the remainder is 1, so 1593 is not a divisor of 1594)
1594 / 1594 = 1 (the remainder is 0, so 1594 is a divisor of 1594)

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 1594 (i.e. 39.924929555354). 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 $\frac{N}{d} = D$ )

1594 / 1 = 1594 (the remainder is 0, so 1 and 1594 are divisors of 1594)
1594 / 2 = 797 (the remainder is 0, so 2 and 797 are divisors of 1594)
1594 / 3 = 531.33333333333 (the remainder is 1, so 3 is not a divisor of 1594)
...
1594 / 38 = 41.947368421053 (the remainder is 36, so 38 is not a divisor of 1594)
1594 / 39 = 40.871794871795 (the remainder is 34, so 39 is not a divisor of 1594)