What are the divisors of 2038?

1, 2, 1019, 2038

There is a total of 4 positive divisors.
The sum of these divisors is 3060.
The arithmetic mean is 765.

2 even divisors

2, 2038

2 odd divisors

1, 1019

How to compute the divisors of 2038?

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 2038 by each of the numbers from 1 to 2038 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)

2038 / 1 = 2038 (the remainder is 0, so 1 is a divisor of 2038)
2038 / 2 = 1019 (the remainder is 0, so 2 is a divisor of 2038)
2038 / 3 = 679.33333333333 (the remainder is 1, so 3 is not a divisor of 2038)
...
2038 / 2037 = 1.0004909180167 (the remainder is 1, so 2037 is not a divisor of 2038)
2038 / 2038 = 1 (the remainder is 0, so 2038 is a divisor of 2038)

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 2038 (i.e. 45.144213361183). 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 $\frac{N}{d} = D$ )

2038 / 1 = 2038 (the remainder is 0, so 1 and 2038 are divisors of 2038)
2038 / 2 = 1019 (the remainder is 0, so 2 and 1019 are divisors of 2038)
2038 / 3 = 679.33333333333 (the remainder is 1, so 3 is not a divisor of 2038)
...
2038 / 44 = 46.318181818182 (the remainder is 14, so 44 is not a divisor of 2038)
2038 / 45 = 45.288888888889 (the remainder is 13, so 45 is not a divisor of 2038)