What are the divisors of 1081?

1, 23, 47, 1081

There is a total of 4 positive divisors.
The sum of these divisors is 1152.
The arithmetic mean is 288.

4 odd divisors

1, 23, 47, 1081

How to compute the divisors of 1081?

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 1081 by each of the numbers from 1 to 1081 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)

1081 / 1 = 1081 (the remainder is 0, so 1 is a divisor of 1081)
1081 / 2 = 540.5 (the remainder is 1, so 2 is not a divisor of 1081)
1081 / 3 = 360.33333333333 (the remainder is 1, so 3 is not a divisor of 1081)
...
1081 / 1080 = 1.0009259259259 (the remainder is 1, so 1080 is not a divisor of 1081)
1081 / 1081 = 1 (the remainder is 0, so 1081 is a divisor of 1081)

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 1081 (i.e. 32.878564445547). 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 $\frac{N}{d} = D$ )

1081 / 1 = 1081 (the remainder is 0, so 1 and 1081 are divisors of 1081)
1081 / 2 = 540.5 (the remainder is 1, so 2 is not a divisor of 1081)
1081 / 3 = 360.33333333333 (the remainder is 1, so 3 is not a divisor of 1081)
...
1081 / 31 = 34.870967741935 (the remainder is 27, so 31 is not a divisor of 1081)
1081 / 32 = 33.78125 (the remainder is 25, so 32 is not a divisor of 1081)