What are the divisors of 2574?

1, 2, 3, 6, 9, 11, 13, 18, 22, 26, 33, 39, 66, 78, 99, 117, 143, 198, 234, 286, 429, 858, 1287, 2574

There is a total of 24 positive divisors.
The sum of these divisors is 6552.
The arithmetic mean is 273.

12 even divisors

2, 6, 18, 22, 26, 66, 78, 198, 234, 286, 858, 2574

12 odd divisors

1, 3, 9, 11, 13, 33, 39, 99, 117, 143, 429, 1287

How to compute the divisors of 2574?

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 2574 by each of the numbers from 1 to 2574 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)

2574 / 1 = 2574 (the remainder is 0, so 1 is a divisor of 2574)
2574 / 2 = 1287 (the remainder is 0, so 2 is a divisor of 2574)
2574 / 3 = 858 (the remainder is 0, so 3 is a divisor of 2574)
...
2574 / 2573 = 1.0003886513797 (the remainder is 1, so 2573 is not a divisor of 2574)
2574 / 2574 = 1 (the remainder is 0, so 2574 is a divisor of 2574)

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 2574 (i.e. 50.734603575863). 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 $\frac{N}{d} = D$ )

2574 / 1 = 2574 (the remainder is 0, so 1 and 2574 are divisors of 2574)
2574 / 2 = 1287 (the remainder is 0, so 2 and 1287 are divisors of 2574)
2574 / 3 = 858 (the remainder is 0, so 3 and 858 are divisors of 2574)
...
2574 / 49 = 52.530612244898 (the remainder is 26, so 49 is not a divisor of 2574)
2574 / 50 = 51.48 (the remainder is 24, so 50 is not a divisor of 2574)