What are the divisors of 904?

1, 2, 4, 8, 113, 226, 452, 904

There is a total of 8 positive divisors.
The sum of these divisors is 1710.
The arithmetic mean is 213.75.

6 even divisors

2, 4, 8, 226, 452, 904

2 odd divisors

1, 113

How to compute the divisors of 904?

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 904 by each of the numbers from 1 to 904 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)

904 / 1 = 904 (the remainder is 0, so 1 is a divisor of 904)
904 / 2 = 452 (the remainder is 0, so 2 is a divisor of 904)
904 / 3 = 301.33333333333 (the remainder is 1, so 3 is not a divisor of 904)
...
904 / 903 = 1.0011074197121 (the remainder is 1, so 903 is not a divisor of 904)
904 / 904 = 1 (the remainder is 0, so 904 is a divisor of 904)

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 904 (i.e. 30.066592756746). 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 $\frac{N}{d} = D$ )

904 / 1 = 904 (the remainder is 0, so 1 and 904 are divisors of 904)
904 / 2 = 452 (the remainder is 0, so 2 and 452 are divisors of 904)
904 / 3 = 301.33333333333 (the remainder is 1, so 3 is not a divisor of 904)
...
904 / 29 = 31.172413793103 (the remainder is 5, so 29 is not a divisor of 904)
904 / 30 = 30.133333333333 (the remainder is 4, so 30 is not a divisor of 904)