What are the divisors of 1082?

1, 2, 541, 1082

There is a total of 4 positive divisors.
The sum of these divisors is 1626.
The arithmetic mean is 406.5.

2 even divisors

2, 1082

2 odd divisors

1, 541

How to compute the divisors of 1082?

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 1082 by each of the numbers from 1 to 1082 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)

1082 / 1 = 1082 (the remainder is 0, so 1 is a divisor of 1082)
1082 / 2 = 541 (the remainder is 0, so 2 is a divisor of 1082)
1082 / 3 = 360.66666666667 (the remainder is 2, so 3 is not a divisor of 1082)
...
1082 / 1081 = 1.0009250693802 (the remainder is 1, so 1081 is not a divisor of 1082)
1082 / 1082 = 1 (the remainder is 0, so 1082 is a divisor of 1082)

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 1082 (i.e. 32.893768406797). 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 $\frac{N}{d} = D$ )

1082 / 1 = 1082 (the remainder is 0, so 1 and 1082 are divisors of 1082)
1082 / 2 = 541 (the remainder is 0, so 2 and 541 are divisors of 1082)
1082 / 3 = 360.66666666667 (the remainder is 2, so 3 is not a divisor of 1082)
...
1082 / 31 = 34.903225806452 (the remainder is 28, so 31 is not a divisor of 1082)
1082 / 32 = 33.8125 (the remainder is 26, so 32 is not a divisor of 1082)