What are the divisors of 1164?

1, 2, 3, 4, 6, 12, 97, 194, 291, 388, 582, 1164

There is a total of 12 positive divisors.
The sum of these divisors is 2744.
The arithmetic mean is 228.66666666667.

8 even divisors

2, 4, 6, 12, 194, 388, 582, 1164

4 odd divisors

1, 3, 97, 291

How to compute the divisors of 1164?

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 1164 by each of the numbers from 1 to 1164 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)

1164 / 1 = 1164 (the remainder is 0, so 1 is a divisor of 1164)
1164 / 2 = 582 (the remainder is 0, so 2 is a divisor of 1164)
1164 / 3 = 388 (the remainder is 0, so 3 is a divisor of 1164)
...
1164 / 1163 = 1.0008598452279 (the remainder is 1, so 1163 is not a divisor of 1164)
1164 / 1164 = 1 (the remainder is 0, so 1164 is a divisor of 1164)

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 1164 (i.e. 34.117444218464). 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 $\frac{N}{d} = D$ )

1164 / 1 = 1164 (the remainder is 0, so 1 and 1164 are divisors of 1164)
1164 / 2 = 582 (the remainder is 0, so 2 and 582 are divisors of 1164)
1164 / 3 = 388 (the remainder is 0, so 3 and 388 are divisors of 1164)
...
1164 / 33 = 35.272727272727 (the remainder is 9, so 33 is not a divisor of 1164)
1164 / 34 = 34.235294117647 (the remainder is 8, so 34 is not a divisor of 1164)