What are the divisors of 1389?

1, 3, 463, 1389

There is a total of 4 positive divisors.
The sum of these divisors is 1856.
The arithmetic mean is 464.

4 odd divisors

1, 3, 463, 1389

How to compute the divisors of 1389?

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 1389 by each of the numbers from 1 to 1389 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)

1389 / 1 = 1389 (the remainder is 0, so 1 is a divisor of 1389)
1389 / 2 = 694.5 (the remainder is 1, so 2 is not a divisor of 1389)
1389 / 3 = 463 (the remainder is 0, so 3 is a divisor of 1389)
...
1389 / 1388 = 1.0007204610951 (the remainder is 1, so 1388 is not a divisor of 1389)
1389 / 1389 = 1 (the remainder is 0, so 1389 is a divisor of 1389)

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 1389 (i.e. 37.269290307168). 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 $\frac{N}{d} = D$ )

1389 / 1 = 1389 (the remainder is 0, so 1 and 1389 are divisors of 1389)
1389 / 2 = 694.5 (the remainder is 1, so 2 is not a divisor of 1389)
1389 / 3 = 463 (the remainder is 0, so 3 and 463 are divisors of 1389)
...
1389 / 36 = 38.583333333333 (the remainder is 21, so 36 is not a divisor of 1389)
1389 / 37 = 37.540540540541 (the remainder is 20, so 37 is not a divisor of 1389)