What are the divisors of 1183?

1, 7, 13, 91, 169, 1183

There is a total of 6 positive divisors.
The sum of these divisors is 1464.
The arithmetic mean is 244.

6 odd divisors

1, 7, 13, 91, 169, 1183

How to compute the divisors of 1183?

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 1183 by each of the numbers from 1 to 1183 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)

1183 / 1 = 1183 (the remainder is 0, so 1 is a divisor of 1183)
1183 / 2 = 591.5 (the remainder is 1, so 2 is not a divisor of 1183)
1183 / 3 = 394.33333333333 (the remainder is 1, so 3 is not a divisor of 1183)
...
1183 / 1182 = 1.0008460236887 (the remainder is 1, so 1182 is not a divisor of 1183)
1183 / 1183 = 1 (the remainder is 0, so 1183 is a divisor of 1183)

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 1183 (i.e. 34.39476704384). 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 $\frac{N}{d} = D$ )

1183 / 1 = 1183 (the remainder is 0, so 1 and 1183 are divisors of 1183)
1183 / 2 = 591.5 (the remainder is 1, so 2 is not a divisor of 1183)
1183 / 3 = 394.33333333333 (the remainder is 1, so 3 is not a divisor of 1183)
...
1183 / 33 = 35.848484848485 (the remainder is 28, so 33 is not a divisor of 1183)
1183 / 34 = 34.794117647059 (the remainder is 27, so 34 is not a divisor of 1183)