What are the divisors of 7044?

1, 2, 3, 4, 6, 12, 587, 1174, 1761, 2348, 3522, 7044

There is a total of 12 positive divisors.
The sum of these divisors is 16464.
The arithmetic mean is 1372.

8 even divisors

2, 4, 6, 12, 1174, 2348, 3522, 7044

4 odd divisors

1, 3, 587, 1761

How to compute the divisors of 7044?

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 7044 by each of the numbers from 1 to 7044 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)

7044 / 1 = 7044 (the remainder is 0, so 1 is a divisor of 7044)
7044 / 2 = 3522 (the remainder is 0, so 2 is a divisor of 7044)
7044 / 3 = 2348 (the remainder is 0, so 3 is a divisor of 7044)
...
7044 / 7043 = 1.0001419849496 (the remainder is 1, so 7043 is not a divisor of 7044)
7044 / 7044 = 1 (the remainder is 0, so 7044 is a divisor of 7044)

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 7044 (i.e. 83.928541033429). 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 $\frac{N}{d} = D$ )

7044 / 1 = 7044 (the remainder is 0, so 1 and 7044 are divisors of 7044)
7044 / 2 = 3522 (the remainder is 0, so 2 and 3522 are divisors of 7044)
7044 / 3 = 2348 (the remainder is 0, so 3 and 2348 are divisors of 7044)
...
7044 / 82 = 85.90243902439 (the remainder is 74, so 82 is not a divisor of 7044)
7044 / 83 = 84.867469879518 (the remainder is 72, so 83 is not a divisor of 7044)