What are the divisors of 1084?

1, 2, 4, 271, 542, 1084

There is a total of 6 positive divisors.
The sum of these divisors is 1904.
The arithmetic mean is 317.33333333333.

4 even divisors

2, 4, 542, 1084

2 odd divisors

1, 271

How to compute the divisors of 1084?

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 1084 by each of the numbers from 1 to 1084 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)

1084 / 1 = 1084 (the remainder is 0, so 1 is a divisor of 1084)
1084 / 2 = 542 (the remainder is 0, so 2 is a divisor of 1084)
1084 / 3 = 361.33333333333 (the remainder is 1, so 3 is not a divisor of 1084)
...
1084 / 1083 = 1.0009233610342 (the remainder is 1, so 1083 is not a divisor of 1084)
1084 / 1084 = 1 (the remainder is 0, so 1084 is a divisor of 1084)

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 1084 (i.e. 32.924155266309). 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 $\frac{N}{d} = D$ )

1084 / 1 = 1084 (the remainder is 0, so 1 and 1084 are divisors of 1084)
1084 / 2 = 542 (the remainder is 0, so 2 and 542 are divisors of 1084)
1084 / 3 = 361.33333333333 (the remainder is 1, so 3 is not a divisor of 1084)
...
1084 / 31 = 34.967741935484 (the remainder is 30, so 31 is not a divisor of 1084)
1084 / 32 = 33.875 (the remainder is 28, so 32 is not a divisor of 1084)