What are the divisors of 1287?

1, 3, 9, 11, 13, 33, 39, 99, 117, 143, 429, 1287

There is a total of 12 positive divisors.
The sum of these divisors is 2184.
The arithmetic mean is 182.

12 odd divisors

1, 3, 9, 11, 13, 33, 39, 99, 117, 143, 429, 1287

How to compute the divisors of 1287?

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 1287 by each of the numbers from 1 to 1287 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)

1287 / 1 = 1287 (the remainder is 0, so 1 is a divisor of 1287)
1287 / 2 = 643.5 (the remainder is 1, so 2 is not a divisor of 1287)
1287 / 3 = 429 (the remainder is 0, so 3 is a divisor of 1287)
...
1287 / 1286 = 1.0007776049767 (the remainder is 1, so 1286 is not a divisor of 1287)
1287 / 1287 = 1 (the remainder is 0, so 1287 is a divisor of 1287)

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 1287 (i.e. 35.874782229304). 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 $\frac{N}{d} = D$ )

1287 / 1 = 1287 (the remainder is 0, so 1 and 1287 are divisors of 1287)
1287 / 2 = 643.5 (the remainder is 1, so 2 is not a divisor of 1287)
1287 / 3 = 429 (the remainder is 0, so 3 and 429 are divisors of 1287)
...
1287 / 34 = 37.852941176471 (the remainder is 29, so 34 is not a divisor of 1287)
1287 / 35 = 36.771428571429 (the remainder is 27, so 35 is not a divisor of 1287)