What are the divisors of 1181?

1, 1181

There is a total of 2 positive divisors.
The sum of these divisors is 1182.
The arithmetic mean is 591.

2 odd divisors

1, 1181

How to compute the divisors of 1181?

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 1181 by each of the numbers from 1 to 1181 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)

1181 / 1 = 1181 (the remainder is 0, so 1 is a divisor of 1181)
1181 / 2 = 590.5 (the remainder is 1, so 2 is not a divisor of 1181)
1181 / 3 = 393.66666666667 (the remainder is 2, so 3 is not a divisor of 1181)
...
1181 / 1180 = 1.0008474576271 (the remainder is 1, so 1180 is not a divisor of 1181)
1181 / 1181 = 1 (the remainder is 0, so 1181 is a divisor of 1181)

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 1181 (i.e. 34.365680554879). 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 $\frac{N}{d} = D$ )

1181 / 1 = 1181 (the remainder is 0, so 1 and 1181 are divisors of 1181)
1181 / 2 = 590.5 (the remainder is 1, so 2 is not a divisor of 1181)
1181 / 3 = 393.66666666667 (the remainder is 2, so 3 is not a divisor of 1181)
...
1181 / 33 = 35.787878787879 (the remainder is 26, so 33 is not a divisor of 1181)
1181 / 34 = 34.735294117647 (the remainder is 25, so 34 is not a divisor of 1181)