What are the divisors of 1186?

1, 2, 593, 1186

There is a total of 4 positive divisors.
The sum of these divisors is 1782.
The arithmetic mean is 445.5.

2 even divisors

2, 1186

2 odd divisors

1, 593

How to compute the divisors of 1186?

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 1186 by each of the numbers from 1 to 1186 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)

1186 / 1 = 1186 (the remainder is 0, so 1 is a divisor of 1186)
1186 / 2 = 593 (the remainder is 0, so 2 is a divisor of 1186)
1186 / 3 = 395.33333333333 (the remainder is 1, so 3 is not a divisor of 1186)
...
1186 / 1185 = 1.0008438818565 (the remainder is 1, so 1185 is not a divisor of 1186)
1186 / 1186 = 1 (the remainder is 0, so 1186 is a divisor of 1186)

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 1186 (i.e. 34.438350715445). 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 $\frac{N}{d} = D$ )

1186 / 1 = 1186 (the remainder is 0, so 1 and 1186 are divisors of 1186)
1186 / 2 = 593 (the remainder is 0, so 2 and 593 are divisors of 1186)
1186 / 3 = 395.33333333333 (the remainder is 1, so 3 is not a divisor of 1186)
...
1186 / 33 = 35.939393939394 (the remainder is 31, so 33 is not a divisor of 1186)
1186 / 34 = 34.882352941176 (the remainder is 30, so 34 is not a divisor of 1186)