What are the divisors of 905?

1, 5, 181, 905

There is a total of 4 positive divisors.
The sum of these divisors is 1092.
The arithmetic mean is 273.

4 odd divisors

1, 5, 181, 905

How to compute the divisors of 905?

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 905 by each of the numbers from 1 to 905 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)

905 / 1 = 905 (the remainder is 0, so 1 is a divisor of 905)
905 / 2 = 452.5 (the remainder is 1, so 2 is not a divisor of 905)
905 / 3 = 301.66666666667 (the remainder is 2, so 3 is not a divisor of 905)
...
905 / 904 = 1.0011061946903 (the remainder is 1, so 904 is not a divisor of 905)
905 / 905 = 1 (the remainder is 0, so 905 is a divisor of 905)

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 905 (i.e. 30.083217912983). 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 $\frac{N}{d} = D$ )

905 / 1 = 905 (the remainder is 0, so 1 and 905 are divisors of 905)
905 / 2 = 452.5 (the remainder is 1, so 2 is not a divisor of 905)
905 / 3 = 301.66666666667 (the remainder is 2, so 3 is not a divisor of 905)
...
905 / 29 = 31.206896551724 (the remainder is 6, so 29 is not a divisor of 905)
905 / 30 = 30.166666666667 (the remainder is 5, so 30 is not a divisor of 905)