What are the divisors of 1161?

1, 3, 9, 27, 43, 129, 387, 1161

There is a total of 8 positive divisors.
The sum of these divisors is 1760.
The arithmetic mean is 220.

8 odd divisors

1, 3, 9, 27, 43, 129, 387, 1161

How to compute the divisors of 1161?

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 1161 by each of the numbers from 1 to 1161 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)

1161 / 1 = 1161 (the remainder is 0, so 1 is a divisor of 1161)
1161 / 2 = 580.5 (the remainder is 1, so 2 is not a divisor of 1161)
1161 / 3 = 387 (the remainder is 0, so 3 is a divisor of 1161)
...
1161 / 1160 = 1.0008620689655 (the remainder is 1, so 1160 is not a divisor of 1161)
1161 / 1161 = 1 (the remainder is 0, so 1161 is a divisor of 1161)

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 1161 (i.e. 34.073450074802). 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 $\frac{N}{d} = D$ )

1161 / 1 = 1161 (the remainder is 0, so 1 and 1161 are divisors of 1161)
1161 / 2 = 580.5 (the remainder is 1, so 2 is not a divisor of 1161)
1161 / 3 = 387 (the remainder is 0, so 3 and 387 are divisors of 1161)
...
1161 / 33 = 35.181818181818 (the remainder is 6, so 33 is not a divisor of 1161)
1161 / 34 = 34.147058823529 (the remainder is 5, so 34 is not a divisor of 1161)