What are the divisors of 574?

1, 2, 7, 14, 41, 82, 287, 574

There is a total of 8 positive divisors.
The sum of these divisors is 1008.
The arithmetic mean is 126.

4 even divisors

2, 14, 82, 574

4 odd divisors

1, 7, 41, 287

How to compute the divisors of 574?

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 574 by each of the numbers from 1 to 574 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)

574 / 1 = 574 (the remainder is 0, so 1 is a divisor of 574)
574 / 2 = 287 (the remainder is 0, so 2 is a divisor of 574)
574 / 3 = 191.33333333333 (the remainder is 1, so 3 is not a divisor of 574)
...
574 / 573 = 1.0017452006981 (the remainder is 1, so 573 is not a divisor of 574)
574 / 574 = 1 (the remainder is 0, so 574 is a divisor of 574)

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 574 (i.e. 23.958297101422). 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 $\frac{N}{d} = D$ )

574 / 1 = 574 (the remainder is 0, so 1 and 574 are divisors of 574)
574 / 2 = 287 (the remainder is 0, so 2 and 287 are divisors of 574)
574 / 3 = 191.33333333333 (the remainder is 1, so 3 is not a divisor of 574)
...
574 / 22 = 26.090909090909 (the remainder is 2, so 22 is not a divisor of 574)
574 / 23 = 24.95652173913 (the remainder is 22, so 23 is not a divisor of 574)