What are the divisors of 1189?

1, 29, 41, 1189

There is a total of 4 positive divisors.
The sum of these divisors is 1260.
The arithmetic mean is 315.

4 odd divisors

1, 29, 41, 1189

How to compute the divisors of 1189?

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 1189 by each of the numbers from 1 to 1189 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)

1189 / 1 = 1189 (the remainder is 0, so 1 is a divisor of 1189)
1189 / 2 = 594.5 (the remainder is 1, so 2 is not a divisor of 1189)
1189 / 3 = 396.33333333333 (the remainder is 1, so 3 is not a divisor of 1189)
...
1189 / 1188 = 1.0008417508418 (the remainder is 1, so 1188 is not a divisor of 1189)
1189 / 1189 = 1 (the remainder is 0, so 1189 is a divisor of 1189)

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 1189 (i.e. 34.481879299133). 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 $\frac{N}{d} = D$ )

1189 / 1 = 1189 (the remainder is 0, so 1 and 1189 are divisors of 1189)
1189 / 2 = 594.5 (the remainder is 1, so 2 is not a divisor of 1189)
1189 / 3 = 396.33333333333 (the remainder is 1, so 3 is not a divisor of 1189)
...
1189 / 33 = 36.030303030303 (the remainder is 1, so 33 is not a divisor of 1189)
1189 / 34 = 34.970588235294 (the remainder is 33, so 34 is not a divisor of 1189)