What are the divisors of 923?

1, 13, 71, 923

There is a total of 4 positive divisors.
The sum of these divisors is 1008.
The arithmetic mean is 252.

4 odd divisors

1, 13, 71, 923

How to compute the divisors of 923?

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 923 by each of the numbers from 1 to 923 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)

923 / 1 = 923 (the remainder is 0, so 1 is a divisor of 923)
923 / 2 = 461.5 (the remainder is 1, so 2 is not a divisor of 923)
923 / 3 = 307.66666666667 (the remainder is 2, so 3 is not a divisor of 923)
...
923 / 922 = 1.0010845986985 (the remainder is 1, so 922 is not a divisor of 923)
923 / 923 = 1 (the remainder is 0, so 923 is a divisor of 923)

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 923 (i.e. 30.380915061927). 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 $\frac{N}{d} = D$ )

923 / 1 = 923 (the remainder is 0, so 1 and 923 are divisors of 923)
923 / 2 = 461.5 (the remainder is 1, so 2 is not a divisor of 923)
923 / 3 = 307.66666666667 (the remainder is 2, so 3 is not a divisor of 923)
...
923 / 29 = 31.827586206897 (the remainder is 24, so 29 is not a divisor of 923)
923 / 30 = 30.766666666667 (the remainder is 23, so 30 is not a divisor of 923)