What are the divisors of 1103?

1, 1103

There is a total of 2 positive divisors.
The sum of these divisors is 1104.
The arithmetic mean is 552.

2 odd divisors

1, 1103

How to compute the divisors of 1103?

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 1103 by each of the numbers from 1 to 1103 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)

1103 / 1 = 1103 (the remainder is 0, so 1 is a divisor of 1103)
1103 / 2 = 551.5 (the remainder is 1, so 2 is not a divisor of 1103)
1103 / 3 = 367.66666666667 (the remainder is 2, so 3 is not a divisor of 1103)
...
1103 / 1102 = 1.0009074410163 (the remainder is 1, so 1102 is not a divisor of 1103)
1103 / 1103 = 1 (the remainder is 0, so 1103 is a divisor of 1103)

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 1103 (i.e. 33.211443810831). 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 $\frac{N}{d} = D$ )

1103 / 1 = 1103 (the remainder is 0, so 1 and 1103 are divisors of 1103)
1103 / 2 = 551.5 (the remainder is 1, so 2 is not a divisor of 1103)
1103 / 3 = 367.66666666667 (the remainder is 2, so 3 is not a divisor of 1103)
...
1103 / 32 = 34.46875 (the remainder is 15, so 32 is not a divisor of 1103)
1103 / 33 = 33.424242424242 (the remainder is 14, so 33 is not a divisor of 1103)