What are the divisors of 3039?

1, 3, 1013, 3039

There is a total of 4 positive divisors.
The sum of these divisors is 4056.
The arithmetic mean is 1014.

4 odd divisors

1, 3, 1013, 3039

How to compute the divisors of 3039?

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 3039 by each of the numbers from 1 to 3039 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)

3039 / 1 = 3039 (the remainder is 0, so 1 is a divisor of 3039)
3039 / 2 = 1519.5 (the remainder is 1, so 2 is not a divisor of 3039)
3039 / 3 = 1013 (the remainder is 0, so 3 is a divisor of 3039)
...
3039 / 3038 = 1.0003291639236 (the remainder is 1, so 3038 is not a divisor of 3039)
3039 / 3039 = 1 (the remainder is 0, so 3039 is a divisor of 3039)

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 3039 (i.e. 55.127125809351). 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 $\frac{N}{d} = D$ )

3039 / 1 = 3039 (the remainder is 0, so 1 and 3039 are divisors of 3039)
3039 / 2 = 1519.5 (the remainder is 1, so 2 is not a divisor of 3039)
3039 / 3 = 1013 (the remainder is 0, so 3 and 1013 are divisors of 3039)
...
3039 / 54 = 56.277777777778 (the remainder is 15, so 54 is not a divisor of 3039)
3039 / 55 = 55.254545454545 (the remainder is 14, so 55 is not a divisor of 3039)