What are the divisors of 906?

1, 2, 3, 6, 151, 302, 453, 906

There is a total of 8 positive divisors.
The sum of these divisors is 1824.
The arithmetic mean is 228.

4 even divisors

2, 6, 302, 906

4 odd divisors

1, 3, 151, 453

How to compute the divisors of 906?

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 906 by each of the numbers from 1 to 906 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)

906 / 1 = 906 (the remainder is 0, so 1 is a divisor of 906)
906 / 2 = 453 (the remainder is 0, so 2 is a divisor of 906)
906 / 3 = 302 (the remainder is 0, so 3 is a divisor of 906)
...
906 / 905 = 1.0011049723757 (the remainder is 1, so 905 is not a divisor of 906)
906 / 906 = 1 (the remainder is 0, so 906 is a divisor of 906)

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 906 (i.e. 30.099833886585). 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 $\frac{N}{d} = D$ )

906 / 1 = 906 (the remainder is 0, so 1 and 906 are divisors of 906)
906 / 2 = 453 (the remainder is 0, so 2 and 453 are divisors of 906)
906 / 3 = 302 (the remainder is 0, so 3 and 302 are divisors of 906)
...
906 / 29 = 31.241379310345 (the remainder is 7, so 29 is not a divisor of 906)
906 / 30 = 30.2 (the remainder is 6, so 30 is not a divisor of 906)