What are the divisors of 1187?

1, 1187

There is a total of 2 positive divisors.
The sum of these divisors is 1188.
The arithmetic mean is 594.

2 odd divisors

1, 1187

How to compute the divisors of 1187?

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 1187 by each of the numbers from 1 to 1187 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)

1187 / 1 = 1187 (the remainder is 0, so 1 is a divisor of 1187)
1187 / 2 = 593.5 (the remainder is 1, so 2 is not a divisor of 1187)
1187 / 3 = 395.66666666667 (the remainder is 2, so 3 is not a divisor of 1187)
...
1187 / 1186 = 1.0008431703204 (the remainder is 1, so 1186 is not a divisor of 1187)
1187 / 1187 = 1 (the remainder is 0, so 1187 is a divisor of 1187)

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 1187 (i.e. 34.452866353904). 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 $\frac{N}{d} = D$ )

1187 / 1 = 1187 (the remainder is 0, so 1 and 1187 are divisors of 1187)
1187 / 2 = 593.5 (the remainder is 1, so 2 is not a divisor of 1187)
1187 / 3 = 395.66666666667 (the remainder is 2, so 3 is not a divisor of 1187)
...
1187 / 33 = 35.969696969697 (the remainder is 32, so 33 is not a divisor of 1187)
1187 / 34 = 34.911764705882 (the remainder is 31, so 34 is not a divisor of 1187)