What are the divisors of 2084?

1, 2, 4, 521, 1042, 2084

There is a total of 6 positive divisors.
The sum of these divisors is 3654.
The arithmetic mean is 609.

4 even divisors

2, 4, 1042, 2084

2 odd divisors

1, 521

How to compute the divisors of 2084?

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 2084 by each of the numbers from 1 to 2084 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)

2084 / 1 = 2084 (the remainder is 0, so 1 is a divisor of 2084)
2084 / 2 = 1042 (the remainder is 0, so 2 is a divisor of 2084)
2084 / 3 = 694.66666666667 (the remainder is 2, so 3 is not a divisor of 2084)
...
2084 / 2083 = 1.0004800768123 (the remainder is 1, so 2083 is not a divisor of 2084)
2084 / 2084 = 1 (the remainder is 0, so 2084 is a divisor of 2084)

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 2084 (i.e. 45.650848842053). 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 $\frac{N}{d} = D$ )

2084 / 1 = 2084 (the remainder is 0, so 1 and 2084 are divisors of 2084)
2084 / 2 = 1042 (the remainder is 0, so 2 and 1042 are divisors of 2084)
2084 / 3 = 694.66666666667 (the remainder is 2, so 3 is not a divisor of 2084)
...
2084 / 44 = 47.363636363636 (the remainder is 16, so 44 is not a divisor of 2084)
2084 / 45 = 46.311111111111 (the remainder is 14, so 45 is not a divisor of 2084)