What are the divisors of 1133?

1, 11, 103, 1133

There is a total of 4 positive divisors.
The sum of these divisors is 1248.
The arithmetic mean is 312.

4 odd divisors

1, 11, 103, 1133

How to compute the divisors of 1133?

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 1133 by each of the numbers from 1 to 1133 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)

1133 / 1 = 1133 (the remainder is 0, so 1 is a divisor of 1133)
1133 / 2 = 566.5 (the remainder is 1, so 2 is not a divisor of 1133)
1133 / 3 = 377.66666666667 (the remainder is 2, so 3 is not a divisor of 1133)
...
1133 / 1132 = 1.0008833922261 (the remainder is 1, so 1132 is not a divisor of 1133)
1133 / 1133 = 1 (the remainder is 0, so 1133 is a divisor of 1133)

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 1133 (i.e. 33.660065359414). 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 $\frac{N}{d} = D$ )

1133 / 1 = 1133 (the remainder is 0, so 1 and 1133 are divisors of 1133)
1133 / 2 = 566.5 (the remainder is 1, so 2 is not a divisor of 1133)
1133 / 3 = 377.66666666667 (the remainder is 2, so 3 is not a divisor of 1133)
...
1133 / 32 = 35.40625 (the remainder is 13, so 32 is not a divisor of 1133)
1133 / 33 = 34.333333333333 (the remainder is 11, so 33 is not a divisor of 1133)