What are the divisors of 1558?

1, 2, 19, 38, 41, 82, 779, 1558

There is a total of 8 positive divisors.
The sum of these divisors is 2520.
The arithmetic mean is 315.

4 even divisors

2, 38, 82, 1558

4 odd divisors

1, 19, 41, 779

How to compute the divisors of 1558?

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 1558 by each of the numbers from 1 to 1558 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)

1558 / 1 = 1558 (the remainder is 0, so 1 is a divisor of 1558)
1558 / 2 = 779 (the remainder is 0, so 2 is a divisor of 1558)
1558 / 3 = 519.33333333333 (the remainder is 1, so 3 is not a divisor of 1558)
...
1558 / 1557 = 1.0006422607579 (the remainder is 1, so 1557 is not a divisor of 1558)
1558 / 1558 = 1 (the remainder is 0, so 1558 is a divisor of 1558)

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 1558 (i.e. 39.471508711981). 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 $\frac{N}{d} = D$ )

1558 / 1 = 1558 (the remainder is 0, so 1 and 1558 are divisors of 1558)
1558 / 2 = 779 (the remainder is 0, so 2 and 779 are divisors of 1558)
1558 / 3 = 519.33333333333 (the remainder is 1, so 3 is not a divisor of 1558)
...
1558 / 38 = 41 (the remainder is 0, so 38 and 41 are divisors of 1558)
1558 / 39 = 39.948717948718 (the remainder is 37, so 39 is not a divisor of 1558)