What are the divisors of 1180?

1, 2, 4, 5, 10, 20, 59, 118, 236, 295, 590, 1180

There is a total of 12 positive divisors.
The sum of these divisors is 2520.
The arithmetic mean is 210.

8 even divisors

2, 4, 10, 20, 118, 236, 590, 1180

4 odd divisors

1, 5, 59, 295

How to compute the divisors of 1180?

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 1180 by each of the numbers from 1 to 1180 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)

1180 / 1 = 1180 (the remainder is 0, so 1 is a divisor of 1180)
1180 / 2 = 590 (the remainder is 0, so 2 is a divisor of 1180)
1180 / 3 = 393.33333333333 (the remainder is 1, so 3 is not a divisor of 1180)
...
1180 / 1179 = 1.0008481764207 (the remainder is 1, so 1179 is not a divisor of 1180)
1180 / 1180 = 1 (the remainder is 0, so 1180 is a divisor of 1180)

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 1180 (i.e. 34.351128074635). 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 $\frac{N}{d} = D$ )

1180 / 1 = 1180 (the remainder is 0, so 1 and 1180 are divisors of 1180)
1180 / 2 = 590 (the remainder is 0, so 2 and 590 are divisors of 1180)
1180 / 3 = 393.33333333333 (the remainder is 1, so 3 is not a divisor of 1180)
...
1180 / 33 = 35.757575757576 (the remainder is 25, so 33 is not a divisor of 1180)
1180 / 34 = 34.705882352941 (the remainder is 24, so 34 is not a divisor of 1180)