What are the divisors of 1383?

1, 3, 461, 1383

There is a total of 4 positive divisors.
The sum of these divisors is 1848.
The arithmetic mean is 462.

4 odd divisors

1, 3, 461, 1383

How to compute the divisors of 1383?

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 1383 by each of the numbers from 1 to 1383 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)

1383 / 1 = 1383 (the remainder is 0, so 1 is a divisor of 1383)
1383 / 2 = 691.5 (the remainder is 1, so 2 is not a divisor of 1383)
1383 / 3 = 461 (the remainder is 0, so 3 is a divisor of 1383)
...
1383 / 1382 = 1.0007235890014 (the remainder is 1, so 1382 is not a divisor of 1383)
1383 / 1383 = 1 (the remainder is 0, so 1383 is a divisor of 1383)

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 1383 (i.e. 37.188707963574). 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 $\frac{N}{d} = D$ )

1383 / 1 = 1383 (the remainder is 0, so 1 and 1383 are divisors of 1383)
1383 / 2 = 691.5 (the remainder is 1, so 2 is not a divisor of 1383)
1383 / 3 = 461 (the remainder is 0, so 3 and 461 are divisors of 1383)
...
1383 / 36 = 38.416666666667 (the remainder is 15, so 36 is not a divisor of 1383)
1383 / 37 = 37.378378378378 (the remainder is 14, so 37 is not a divisor of 1383)