What are the divisors of 3028?

1, 2, 4, 757, 1514, 3028

There is a total of 6 positive divisors.
The sum of these divisors is 5306.
The arithmetic mean is 884.33333333333.

4 even divisors

2, 4, 1514, 3028

2 odd divisors

1, 757

How to compute the divisors of 3028?

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 3028 by each of the numbers from 1 to 3028 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)

3028 / 1 = 3028 (the remainder is 0, so 1 is a divisor of 3028)
3028 / 2 = 1514 (the remainder is 0, so 2 is a divisor of 3028)
3028 / 3 = 1009.3333333333 (the remainder is 1, so 3 is not a divisor of 3028)
...
3028 / 3027 = 1.0003303600925 (the remainder is 1, so 3027 is not a divisor of 3028)
3028 / 3028 = 1 (the remainder is 0, so 3028 is a divisor of 3028)

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 3028 (i.e. 55.02726596879). 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 $\frac{N}{d} = D$ )

3028 / 1 = 3028 (the remainder is 0, so 1 and 3028 are divisors of 3028)
3028 / 2 = 1514 (the remainder is 0, so 2 and 1514 are divisors of 3028)
3028 / 3 = 1009.3333333333 (the remainder is 1, so 3 is not a divisor of 3028)
...
3028 / 54 = 56.074074074074 (the remainder is 4, so 54 is not a divisor of 3028)
3028 / 55 = 55.054545454545 (the remainder is 3, so 55 is not a divisor of 3028)