What are the divisors of 2042?

1, 2, 1021, 2042

There is a total of 4 positive divisors.
The sum of these divisors is 3066.
The arithmetic mean is 766.5.

2 even divisors

2, 2042

2 odd divisors

1, 1021

How to compute the divisors of 2042?

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 2042 by each of the numbers from 1 to 2042 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)

2042 / 1 = 2042 (the remainder is 0, so 1 is a divisor of 2042)
2042 / 2 = 1021 (the remainder is 0, so 2 is a divisor of 2042)
2042 / 3 = 680.66666666667 (the remainder is 2, so 3 is not a divisor of 2042)
...
2042 / 2041 = 1.000489955904 (the remainder is 1, so 2041 is not a divisor of 2042)
2042 / 2042 = 1 (the remainder is 0, so 2042 is a divisor of 2042)

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 2042 (i.e. 45.18849411078). 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 $\frac{N}{d} = D$ )

2042 / 1 = 2042 (the remainder is 0, so 1 and 2042 are divisors of 2042)
2042 / 2 = 1021 (the remainder is 0, so 2 and 1021 are divisors of 2042)
2042 / 3 = 680.66666666667 (the remainder is 2, so 3 is not a divisor of 2042)
...
2042 / 44 = 46.409090909091 (the remainder is 18, so 44 is not a divisor of 2042)
2042 / 45 = 45.377777777778 (the remainder is 17, so 45 is not a divisor of 2042)