What are the divisors of 3044?

1, 2, 4, 761, 1522, 3044

There is a total of 6 positive divisors.
The sum of these divisors is 5334.
The arithmetic mean is 889.

4 even divisors

2, 4, 1522, 3044

2 odd divisors

1, 761

How to compute the divisors of 3044?

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 3044 by each of the numbers from 1 to 3044 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)

3044 / 1 = 3044 (the remainder is 0, so 1 is a divisor of 3044)
3044 / 2 = 1522 (the remainder is 0, so 2 is a divisor of 3044)
3044 / 3 = 1014.6666666667 (the remainder is 2, so 3 is not a divisor of 3044)
...
3044 / 3043 = 1.0003286230693 (the remainder is 1, so 3043 is not a divisor of 3044)
3044 / 3044 = 1 (the remainder is 0, so 3044 is a divisor of 3044)

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 3044 (i.e. 55.172456896535). 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 $\frac{N}{d} = D$ )

3044 / 1 = 3044 (the remainder is 0, so 1 and 3044 are divisors of 3044)
3044 / 2 = 1522 (the remainder is 0, so 2 and 1522 are divisors of 3044)
3044 / 3 = 1014.6666666667 (the remainder is 2, so 3 is not a divisor of 3044)
...
3044 / 54 = 56.37037037037 (the remainder is 20, so 54 is not a divisor of 3044)
3044 / 55 = 55.345454545455 (the remainder is 19, so 55 is not a divisor of 3044)