What are the divisors of 1191?

1, 3, 397, 1191

There is a total of 4 positive divisors.
The sum of these divisors is 1592.
The arithmetic mean is 398.

4 odd divisors

1, 3, 397, 1191

How to compute the divisors of 1191?

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 1191 by each of the numbers from 1 to 1191 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)

1191 / 1 = 1191 (the remainder is 0, so 1 is a divisor of 1191)
1191 / 2 = 595.5 (the remainder is 1, so 2 is not a divisor of 1191)
1191 / 3 = 397 (the remainder is 0, so 3 is a divisor of 1191)
...
1191 / 1190 = 1.0008403361345 (the remainder is 1, so 1190 is not a divisor of 1191)
1191 / 1191 = 1 (the remainder is 0, so 1191 is a divisor of 1191)

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 1191 (i.e. 34.510867853475). 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 $\frac{N}{d} = D$ )

1191 / 1 = 1191 (the remainder is 0, so 1 and 1191 are divisors of 1191)
1191 / 2 = 595.5 (the remainder is 1, so 2 is not a divisor of 1191)
1191 / 3 = 397 (the remainder is 0, so 3 and 397 are divisors of 1191)
...
1191 / 33 = 36.090909090909 (the remainder is 3, so 33 is not a divisor of 1191)
1191 / 34 = 35.029411764706 (the remainder is 1, so 34 is not a divisor of 1191)