What are the divisors of 939?

1, 3, 313, 939

There is a total of 4 positive divisors.
The sum of these divisors is 1256.
The arithmetic mean is 314.

4 odd divisors

1, 3, 313, 939

How to compute the divisors of 939?

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 939 by each of the numbers from 1 to 939 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)

939 / 1 = 939 (the remainder is 0, so 1 is a divisor of 939)
939 / 2 = 469.5 (the remainder is 1, so 2 is not a divisor of 939)
939 / 3 = 313 (the remainder is 0, so 3 is a divisor of 939)
...
939 / 938 = 1.001066098081 (the remainder is 1, so 938 is not a divisor of 939)
939 / 939 = 1 (the remainder is 0, so 939 is a divisor of 939)

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 939 (i.e. 30.643106892089). 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 $\frac{N}{d} = D$ )

939 / 1 = 939 (the remainder is 0, so 1 and 939 are divisors of 939)
939 / 2 = 469.5 (the remainder is 1, so 2 is not a divisor of 939)
939 / 3 = 313 (the remainder is 0, so 3 and 313 are divisors of 939)
...
939 / 29 = 32.379310344828 (the remainder is 11, so 29 is not a divisor of 939)
939 / 30 = 31.3 (the remainder is 9, so 30 is not a divisor of 939)